Evaluate the definite integral of: * z(r² +1)° dz O 250/6 O 156.25 625/8

Q: Evaluate the definite integral. (Assume a > 0.) ra2/5 x*V a² - x5 dx

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Q: Evaluate the integral by making an appropriate u-substitution and applying any necessary formula(s).…

A: Taking substitution

Q: Evaluate the integral by making an appropriate u-substitution and applying any necessary formula(s).…

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Q: Evaluate the integral 31 by making the substitution u = x° – 4. + C NOTE: Your answer should be in…

A: Given,  ∫ x4x5-431dx

Q: 32 6. f³² x oriz Steuleve

A: Note : As per our guidelines we are supposed to answer only one question if there are multiple…

Q: Evaluate the integral a* (a* – 4)"da - by making the substitution u = x* – 4. + C NOTE: Your answer…

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Q: Write the integral as a sum of integrals without absolute values and evaluate: Sri4 | cos x | dx =…

A: We have, |cos(x)| = cos(x) when, π/4 <= x <= π/2 And, |cos(x)| = - cos(x) when, π/2 <= x…

Q: Evaluate the definite integral. 12 | ri+f j|| dt =

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Q: Evaluate the definite integral using an appropriate u-substitution. cos(x²) dæ 4.87424

A: To Determine: evaluate the definite integral using an appropriate u-substitution Given: we a have…

Q: Evaluate the following integral, where R is bounded by x = 3, y = 3x+ 3, and y = - x- 1. dA Ilỷ dA…

A: J

Q: Evaluate the integral by making an appropriate u-substitution and applying any necessary formula(s).…

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Q: Evaluate the following integrals. Jo cos?

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Q: 2. (a) Use substitution to find indefinite integral. (b) /2re xP i+?

A: Since you have asked multiple questions in single request  so we  will be answering only first…

Q: 1. Jổ xdx xdx ull ch 2. √²2² (x²-x)dx 3. f2, xdx

A: We have to solve as per guidelines Solving by fundamental theorem of calculus

Q: Consider the following the integral from 0 to 0.75 of x^2/sqrt(9-16x^2) dx using trigonometric…

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Q: Evaluate the integral by making an appropriate u-substitution and applying any necessary formula(s).…

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Q: Evaluate the integral by making an appropriate u-substitution and applying any necessary formula(s).…

A: Given : Integral  ∫ex-21x-21dx   To find : Evaluate the given integral by using u-substitution?

Q: Evaluate the definite integral. Si f (x) dæ, f (x) =4"-(7a+ 13)/a?

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Q: Decide whether the integral is improper. 1,01 In(x5) dx

A: We are asked to find whether integral is proper or improper

Q: 10 Sin h (Ux)

A: we have to find integration

Q: Make the given substitution to evaluate the indefinite integral. 28r dr .u= 3-r 3-r'

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Q: Calculate the definite integral by referring to the figure with the indicated areas. [f(x)dx a Area…

A: topic - definite integral area above the x axis is taken as positive in definite integral when…

Q: Evaluate the following indefinite integral. da I In(x) Note: Don't forget your C! And be sure to use…

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Q: Evaluate the following integral by reversing the order. 5/2 1 | 3cosxdydx. "/2 sinx

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Q: ) Compute the following integrals. When a numerical value is sought, leave your answer in symbolic…

A: .................(1) substitute ...............put it back in equation 1

Q: Evaluate this definite integral using a Geometric Formula: J(8-2x dx

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Q: Evaluate the indefinite integral. fr sin (z)cos(z)dz- + C

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Q: Evaluate the following indefinite integral by using Trigonometric Substitutions dx (1-x2) O…

A: As this is a multiple question according to the Bartleby Answering rule, only first question is to…

Q: Evaluate the indefinite integral by using the given substitution to reduce the integral to standard…

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Q: 4x tan(x² }tx

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Q: Evaluate the indefinite integral.

A: To integrate

Q: Evaluate the following integral using trigonometric substitution. /196 – x² dx [/196 - x² dx =| vact…

A: Explanation of the answer is as follows

Q: Evaluate the definite integral. da r(1+ In z)

A: We will use fact that  ln(a)b=b.ln(a). And ln(1)=0.

Q: Evaluate the following definite integral: F () 25 3 da = Number

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Q: Evaluate the indefinite integral by using the substitution u = 5-x' to reduce the integral to…

A: Given the integral

Q: Evaluate the integral by making an appropriate u-substitution and applying any necessary formula(s).…

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Q: Use geometric interpretation of a definite integral to com- pute f, V25 - r²dx and f,"5dx. Draw the…

A: To find the solution

Q: Evaluate the following integral by reversing the order. 5a/2 1 || 3cosxdydx. "½ sinx

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Q: Find the following integral with respect to u, if we use the substitution.8 u = e to evaluate Sede…

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Q: Evaluate the definite integral. Si f (x) dæ, f (x) =3"–(15x³+ 6)/a?

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Q: 36) x7 e-x8 dx

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Q: Evaluate the indefinite integral by using the given substitution to reduce the integral to standard…

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Q: Evaluate the following integral using trigonometric substitution. хах Vx2– x – 1 а.

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Q: Evaluate the integral by making the given substitution. (5x)tan(5x)dx, u = 5x + C

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Q: Evaluate the integral by making an appropriate u-substitution and applying any necessary formula(s).…

A: ∫ex-14×1x-14dx Let us take u= x-14, then differentiating u with respect to x, we get   du = 12x-14dx…

Q: e™ tan (eª) d.x J Vsec2 (e") – 7

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Q: Calculate the definite integral by referring to the figure with the indicated areas. Area A = 1.251…

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Q: Evaluate the given definite integral using appropriate substitution: V2rdr = ... A ... B ...

A: We have to solve the Integral

Q: Evaluate the integral. +C

A: Consider I=∫ln7x2 dx

Q: Evaluate the integral by making the given substitution. x2(sqrt x3+22)dx…

A:

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.