Q4: To evaluate the integral fcos' xdx using the reduction formula of cosinc function

Q: 6x dx D.

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Q: y + 6 -dy (Int. of Rational func.) y² + y 2)

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Q: Find the indefinite integral. Vx +2 -dp- 3 X,

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Q: Evaluate the indefinite integral. | V9 + x2 dx = x* + 9 + + Vx +9 + C

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Q: Evaluate the definite integral by the limit definition

A: Here,

Q: State the Comparison Theorem for Improper Integrals. As well, use it to determine whether I+2 dr…

A: The comparison test states that if limx→∞f(x)g(x) is finite and non-zero, then ∫f(x)dx and ∫g(x)dx…

Q: 1. Approximate the value of each of the following definite integrals using: i. Trapezoidal Rule

A: As per Bartleby's answering policy, we can answer only one question, so kindly post the remaining…

Q: Evaluate the definite integral.

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Q: Verify whether the function g(x) solution of the integral equation R P daft

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Q: Evaluate the integral in terms of Beta function: ∫x^12(1−x)^16 dx    limit: 0 to 1

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Q: 1 Use SUBSTITUTION to evaluate the definite integral to three decimal places. xp- 2x +4

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Q: Use reduction formulas to evaluate the integrals ∫ 8 cos4 2πt dt

A: To solve,    ∫ 8 cos4 2πt dt Using reduction formula.

Q: Make a substitution to express the integrand as a rational function and then evaluate the integral.…

A: To find the integration.

Q: Evaluate the following Integrals using Integration by Partial Fraction. Show all the solution.

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Q: Use the Midpoint Rule with n = 3 to approximate the integral 16 | (- 10x + 2x2) dx 10

A: In this question we will use basic of calculus i.e concept of midpoint rule to approximate the…

Q: 1 dx 1 – x?

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Q: Use symmetry to evaluate the following integral. x' dx -3

A: To find: ∫-33x7dx

Q: (a) Use the Midpoint Rule with n = 6 to approximate integral S³ dx 8 x-6 6 x+8

A: Multiple questions-"As per our guidelines we are suppose to answer only one question.Kindly re-post…

Q: 4) Use the Midpoint Rule to approximate the integral. Then evaluate the actual integral. L(3x - 7)²…

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Q: Queston} $²3 20c x²-4 Composite Trapezoidal rule with n=4 dx. 3.1.1. use the to approximate…

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Q: 2ea dx (ет — 1)2 1

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Q: (a) Use the Midpoint Rule with n = 6 to approximate integral 8 x-6 S8 dx 6 x+8 ?

A: As per the instruction, we will be answering the first question. Given:

Q: (a) '8 dx 2

A: (a)∫268 dx=[8x]26We know that ∫k dx=kx+C            = 8*6 - 8*2            = 32

Q: 4. Use the definition of integration to find (1+2x' ) dx , that is find lim f(x; )Ax

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Q: Find the general indefinite integral. (Use C for the constant of integration.) ∫3v(v2+4)2dx

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Q: Make a substitution to express the integrand as a rational function and then evaluate the integral.…

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Q: Evaluate the indefinite integral. V 4 + x² dx = %D

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Q: – dx x Inx x²+1

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Q: х — 3 х3 -4х

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Q: valuate the integral ∫x2/x3+1dx using an appropriate substitution.

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Q: Evaluate the following definite integral using partial fra x- 1 3 x' + x *

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Q: Use the Midpoint Rule withn= 3 to approximate the integral %3D 13 (- 9z - 3a")daz 9x 3x) dx

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Q: | de P8- メレー Oe dedx

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Q: Evaluate the indefinite integral.

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Q: Evaluate the definite integrals using the graph of ƒ (x) below. 4- y 2- 2 4 10 12 -2- -4- -6- •4 (a)…

A: Given,

Q: Evaluate the integral   upper 4 lower 9 of the (root of x) dx

A: To evaluate the integral

Q: Use the definition of the definite integral to evaluate ∫02 (3x2 +1)dx. Use a right-endpoint…

A: As a first step, let's plot the graph of the curve given to us. Let's call the curve y = f(x) = (3x2…

Q: Evaluate the definite integral by the limit definition.

A: Given: ∫031-2x2dx

Q: 3) Use long division to evaluate the indefinite integral f „s dx.

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Q: Use the Midpoint Rule with n = 4 to approximate the integral. 10 x² dx M4 =

A: The given integral is ∫210x2dx. The mid point rule states that if fxis continuous on [a,b][. Let n…

Q: 9. Use Simpson's Rule to approximate the integral f Vx3 – 1 dx withn = 6.

A: We have to find the value of given integral using Simpson's rule.

Q: Evaluate the integral. (Use C for the constant of integration.) x2 xp V 81 - x2

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Q: dx (4 + x²)²

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Q: Vx2 – 4 dx x2

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Q: Q7. Using Simpson's Rule evaluate the integral (√x+1) dx using 8 subintervals.

A: In this question,  we have to evaluate the integral ∫08x+1dx using 8 subintervals by Simpson's Rule.

Q: Evaluate the indefinite integral dx x(x²+2x+1)

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Q: Use any method to evaluate the integral. x'dx 2 X + 16

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Q: Sx (x² + 4)5 Se3*dx

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Q: Use integration by parts to evaluate the definite integral: ∫3se^-4s ds with an upper limit of -0.9…

A: A=3∫abse-4sds , solving A where a,b are upper and lower limits as per questionIntegrate by parts…

Q: Evaluate the definite integral by the limit definition

A: ∫268dxFormula:∫abcdx=cxab=cb-a   , where c is any constant.