Problem 20  Evaluate the definite integral:  ∫ |x-4x^2|dx=  Upper limit of integration=5 Lower limit of integration=-1

Q: S In(sin(x))dx

A: Given, I=∫lnsinx dx To evaluate I.

Q: 1. Integrate: [x³ sin(2x) dx.

A: As per Bartleby guideline, only the first question has been answered. If you want to get the answer…

Q: PROBLEM 1: int. e^sinx dx/secx PROBLEM 2 : int. e^1/x dx/x2 PROBLEM 3 : int. e^inx dx/x PROBLEM 4 :…

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Q: (24) Evaluate the integral: | Va sin(1 + x/2)dx.

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Q: 5. Evalvate the Intgral S2 cos (2x) - Sin 2x)=

A: To evaluate the integral: ∫2cos22x·sin22x dx Solution: We know that, 1). 2sinθ cosθ=sin2θ 2).…

Q: 1 2y³ .2 бу? dy y²

A: Given: ∫212y3-6y2y2dy

Q: S sin x In(cosx) dx

A: To evaluate the integral: I=∫sin x(ln (cos x)) dx Substitute  cos x=t⇒-sin x dx=dt⇒sin x dx=-dt

Q: Problem 1. Evaluate following definite integrals (apply properties if needed): (x² – 2x + 3) dx x299…

A: We need to calculate the definite integral given in the question.  This can be done as follows:

Q: Find the indefinite integral. ∫ sinh x/(1 + sinh2 x) dx

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Q: Problem No. 1: Evaluate - dx using basic substitution method.

A: First I have used the substitution to make integral easy and then evaluate it.

Q: Problem 13 Evaluate the integral  ∫= (dx)/sqrt(1-x^2) Upper limit of integration= 0.8  Lower limit…

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Q: Integral of sin^3 x dx over cos^4 x

A: In this question we have to find the Integration.

Q: (x² ln x dx

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Q: |(In(x))² dx

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Q: limit x to 0 sin(4t)sec(1000t)/10t

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Q: S" sin" (0.5x)cos (0.5x)dx

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Q: Find integral of sin^2 (x/2) dx with bounds of 0 to pi

A: Find the integral of sin^2 (x/2) dx with the bounds 0 to π.

Q: Question 4 Use Question 2 to compute In(13x) dx. Expressions like e, In(2) should not be x10…

A: Given query is to find value of the integral.

Q: x'+z=et; x(0) = 1

A: Take z as constant

Q: Solve: The integral of (sec(x))^3 dx.

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Q: 3 dx 00 (2²+4)³/2 es or diverges.

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Q: 3) Find the equation of the curve whose arclength from the point (4, 1) to the point (9, -1) is…

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Q: 4. S(x - 1)/sin (2x - x2) cot (2x– x²) dx (Trigonometric Integrals)

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Q: 6. S sin(ln x) dx 7. Show that x" In x dx = 山+ In x + C. n+1 n+1

A: Note: As per the company's guidelines we have to solve only one question. So, kindly post the next…

Q: integral of cos x sin^3 2 x dx

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Q: QUESTION 3 a) Evaluate the integral tanh (2x)sech (2x)dx.

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Q: QUESTION 1 Find (1+2x) In5x² 2x) In 5x² dx by using integration by parts.

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Q: 4.) S dx 1-cosx

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Q: 2 [ 2e sin de

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Q: S sin(3x + 2) cos(1 – 4x)dx

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Q: Problem 7 y = e- dt y/ =? 0.

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Q: Find integral.

A: Given : ∫-5xsinxdx

Q: Find the definite integral from 1 to 3 of |-3x+1| dx

A: According to the given information it is required to find the value of the definite integral.

Q: Find the indefinite integral ∫sinh(1 − 2x) dx

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Q: Problem 2 Use four rectangles and midpoint approximations to find the area for f(x) = cos (x), on…

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Q: Integral of e^(4x)sin(4x) dx

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Q: I Braluate th FOllowing integralis 3+cos (logqx) dx x sin (loga x )

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Q: 4: ystem of differential ec

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Q: INTEGRATE THE FOLLOWING FUNCTION. sinx dx e PROBLEM 1 : secx 1 e* dx PROBLEM 2 :

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: Vsin x.cos x 1+ 2.ln x 3y (аns.: 4

A: Given                   y43= sinx cosx1+2.lnx

Q: 2 sin x f(x) = 1+2cosx 5. Pvaluated at x = 1 rad

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Q: 1 Integrate: S tan*÷x dx 3

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Q: Example 1 Differentiate each of (a) f (x) =2 x' cosh x sinh t (b) h(t)=

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Q: | (In x)² dx_use integrationI

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Q: 1. Use integration by parts to find (3x – 1) sin x dx.

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: integral e 2x sin 3x dx

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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.