Assume that f (x) is a function such that f(x)dx = 2x2 2x + c. - Using trigonometric substitution, compute the integral 6x8 f (x) + 11 (V16 – x² -

Q: Evaluate the integral (2æ + 6)(x² + 6x + 9)*dx by making the substitution u = x? + 6x + 9. + C

A:

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

A:

Q: Evaluate the following definite integral. Assume that B > 1. -в 2х + 8 dx x2 + 8x + 9 /1

A:

Q: By the even extension method applied to the function f (x) = e¬16x, where x > 0, the value of the…

A: We have to solve given problem:

Q: By the odd extension method applied to the function f (x) = e¯2x, wherex > 0, the Fourier integral…

A: Given the function  fx=e-2x

Q: Let a be a constant, Evaluate[ (a* + x² + a) sin(3z") + 15z*)dzr.

A:

Q: 8 cos" 2πt dt

A:

Q: Evaluate the definite integral. ¤(x² + 7)°dx (b) / z x/1 – x²dx (a)

A:

Q: Use the Fundamental Theorem of Calculus to evaluate the following definite integral. V3 2 8 dx V1-x?

A:

Q: Obtain a formula that expresses the integral ∫cosn x dx

A:

Q: The integral of (x® dx) / (xª - 1) is: (xP/8) + [ ↓ 11og[ 플 1+[글]tan'1 x

A: Consider the given integral

Q: Evaluate the definite integral. e !/x5 dx 1 to

A: We have to solve integration by put  1/x⁵ = t

Q: Let F(x) = | sin(7t) dt. 0, Find the MacLaurin polynomial of degree 7 for F(x). 0.71 Use this…

A:

Q: Find constants c1 and c2 such that: F(x) = c1 sin(3x) + c2x cos(3x) is an antiderivative of f(x) =…

A:

Q: Use the Fourier transform methods to evaluate the integral dx (r? +9)(x² +4)

A: In this question, we evaluate the integral by using Fourier transform. The integral is…

Q: 16 – x2 dx - Evaluate the integral: 9x?

A: (A)  x=4sin(θ) (B)  19cot2(θ) (C)  -19θ-19cot(θ) (D)  -19arcsin14x-16-x29x

Q: Suppose F(x)=∫7 to x (sin(t)/4+t) dt. Use the Fundamental of Theorem of Calculus to calculate F′(x).

A:

Q: is stricly increasing on (0, T /2). sin x Prove that the function f(x)=

A: Given that: f(x)=xsinx

Q: Evaluate the integral. x2 cos(6 x) dx + C

A:

Q: Find an antiderivative F(x) of the function f(x)= 6sinx / 12+cosx such that F(0)=1.

A:

Q: Use the residue theorem to evaluate: o dx 0 x3+1 2n/3

A:

Q: The suitable substitution to evaluate the integral V tan (2x) dx is cos (2x) COS

A:

Q: Evaluate the integral f 2x (x2 + 5)" dx using the substitution 16 u = x + 5. 16 2x (x² + 5)" dx = +C

A: Solve integration

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

A:

Q: Prove that for all r € [1, 00), – sinh (- |cosh-(x)|) = vVI² – 1.

A: We know that: Cosh-1x=logex+x2-1  and  Sinhx=ex-e-x2. And, Sinh-x=-Sinhx. Therefore,…

Q: Let F(x) | sin (4t?) dt. Find the MacLaurin polynomial of degree 7 for F(x). 0.8 Use this polynomial…

A:

Q: Demonstrate that for the function of the type va? + x2 you use the substitution X-atane and use it…

A:

Q: -Consider the function defined by the base: Find dz ) Prove that дz +y əx дz ду = sin 2z z =…

A: Topic:- application of derivatives

Q: Evaluate the integral. x2 cos(7 x) dx +C

A: The given integral is: I=∫x2 cos(7x) dx

Q: Use the substitution formula to evaluate the integral. T/16 (1 + etan 4x) sec 2 4x dx 4e

A: Given that ∫0π161+etan4x sec24x dx ...........................(i) Substitute u= 4x  dudx=4 ⇒dx=du4…

Q: The domain of f(x)= sin(In( is

A:

Q: f(z) = cos-1 (포) -er s=(z) – e²

A: Concept of IVT is used while solving this problem.

Q: If f(x)= the definitive integral from 3 to x of (t2+5)1/2dt, find f'(5).

A: Given : fx = ∫3xt2+5

Q: The integral of the function cos² x. sin a dx is

A: the given expression is: ∫cos2x.sinxdx

Q: The Wronskian, W, of the functions y1 = sin(2x) and y2 cos(2x) is %3D

A:

Q: Evaluate the integral dx (2a + 6) by making the appropriate substitution: u = dx (2a+ 6)°

A: I have use the substitution

Q: The integral x dx x² + √x² can be transformed to which of the following using trigonometric…

A: ∫xx2+x2-1-1dx=∫secθ.secθtanθsec2θ+sec2-1-1dθ=∫sec2θtanθsec2θ-1+sec2-1dθ=∫sec2θtanθtan2θ+tanθdθ=∫sec2…

Q: d41 -cosh(x) at x : O is dx41

A: cosh (x)

Q: Find the Fourier integral of the function f(x)= e* when x> 0 and f(-x) = f(x) for k > 0 cosix and…

A: Fourier integral, for even function

Q: The integral S x dx x²+√√x²-1-1 can be transformed to which of the following using trigonometric…

A: Please follow the next step.

Q: Let f(x) = e cosx, sx %3D 2. Express your answers in exact form. ElN

A: Inflection point occurs when the second derivative of the function equals to zero.

Q: Use residue theory to calculate the following integrals: 3x 1. Loo (x² + 49) (x² − 2x+5) (a) P.V. dx

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

Q: Given that f(x) = x² sinx, use Leibniz's theorem to find Ⓒd ²³ f dx²³

A: Here the given function is f(x)=x4sin(x). We have to find the third order differentiation of f(x) by…

Q: Find the integral +C 1 dx x² – 16

A:

Q: Let F(z) = | sin(5t) dt. Find the MacLaurin polynomial of degree 7 for F(z). 0.69 | sin(5z*) dz. Use…

A:

Q: Evaluate the integral cos (x) sin(x) dx 13 using the substitution u = cos(x). cos(x) sin(x) d.x ,13…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Use the three-point Gauss-Legendre formula to evaluate the integral dx Ső (2x + 1)²

A:

Q: 27n 4 cos x sin x dx 7/3

A:

Q: By the odd extension method applied to the function f(x) = e-2=, where a > 0, the Fourier integral…

A: The given function is, f(x)=e-2x,x>0