b. sin? () = 2 over [0, 2n) %3D

Q: Find the indefinite integral: cos ( πx ) dx sin, ( π )

A:

Q: S tan 1x dx

A:

Q: Evaluate the integral (exact value). e2X sin(8x) dx =

A: We have to find the integral.

Q: 7. S tan 5x dx

A: Using integration

Q: e sinh 2x dx

A: The given integral,       ∫e-xsinh(2x) dx

Q: Evaluate the integrals in Exercises

A: ∫-ln20cosh2x2dx∫0ln104sinh2x2dx

Q: -п/8 S sec? (2x)dx

A: We have to evaluate the definite integral: ∫0π8sec22xdx Assuming, t=2x Then definite limit will also…

Q: Fined the inteym Sx cosx da @ S cos?x dx X COSX tan'x dx

A:

Q: Find the indefinite integral.

A:

Q: Estimate sinx? dx with an error of less than 0.001.

A: Given ∫01sin(x2)dx

Q: L[sin bd]- show that

A:

Q: S. 3 Estimate tan x dx using the midpoints of 6 rectangles.

A:

Q: Compute the exact value. 2 dx 2.

A: Simplify the given integral using limits.

Q: Evaluate. S(sin x)e* dx

A:

Q: Suppose y = sin x. What is the x- value between 0 and that corresponds to a y-valué of ? 2 [?]

A: The objective of the question is determine the value of "x" where as y=1/2 in the given function…

Q: S tan — х) dx

A: To integrate: ∫tan(x4-x)dx Solution: Given, ∫tan(x4-x)dx On simplifying further we get:…

Q: tanx . In(cosx) dx

A: we have to evaluate,   I=∫tanx . ln(cosx) dx

Q: Evaluate the inclepinite infegral Cos 3X +3 dx Sin 3x

A:

Q: 5. Sx? cos 6x3 dx %3D

A: We have to evaluate the given integral by using theorems of antidifferentiation.

Q: Find the trigonometric integral ∫x tan4 x2 dx

A: Given: I=∫xtan4x2dx for evaluating given integral, we substitute  x2=t…

Q: "4 rseco sin 20 dp do d0 0. 0,

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Q: y = ln° '(n*))) (tanh²(sec

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Q: What is the area of the region between the sine curve and the x-axis from to 2 ? -1 2 1 4 3.

A: Here we have to find the area of the region bounded by the sine curve and the x-axis from π2 to 2π.…

Q: Find the principal values of tanh(1-j).

A: Use the trigonometric expression for tan (x-y) to expand the given hyperbolic trigonometric…

Q: A. Evaluate. 1 (sinhx - sinhx +coshx cosh?x 1. dx

A:

Q: So Si S*x 1 су-х ху dzdydx

A: Let the integral be  I = ∫01∫x1∫0y-xxydzdydx 'I' can be solved directly by integrating individual…

Q: 8. Using any work found in Question 7, determine the 3x (x? - 5)° dx a.

A:

Q: Evaluate the integral (exact value). e3x sin(10x) dx = %3D

A:

Q: 18 sin a dx

A:

Q: a) | x In ædx

A:

Q: S d0 cosh 0 + sinh

A:

Q: Evaluate the integral (exact value). e3x sin(6x) dx %3D

A: Integration By Parts Formula

Q: 8. Sedr cos 2x dx

A: Integration of e3x cos2x

Q: if x = acos30, y = asin30 , find /1 + 2 dx

A:

Q: Find the antiderivative of sin(square root of 5x)

A: Consider the given function:

Q: 3. tan e de ) 71+ In cose)43

A:

Q: What is wrong with this calculation? 1 dx In |x||, = In 1 - In 1 = 0 - 1

A: The integral of 1xwith respect to x is log(|x|). where x≠0, cause if it is zero then function became…

Q: 6. Se¯*tane¯*sec?e¬*dx

A: To evaluate: I=∫e-xtan(e-x) sec2(e-x) dx=∫tan(e-x) sec2(e-x) (e-x)dx...(1)

Q: a (a) L{sin at}=- s2 +a?

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Q: the da entia Dn.

A:

Q: Evaluate the integral (exact value). e2X sin(8x) dx = %3D

A: We can evaluate the given Integral by using the integration by parts method

Q: Find the numerical value of a) sinh Cen 4) b) sinh (1

A:

Q: 7 dx = x3

A: ∫xndx=xn+1n+1+C1xn=x-n

Q: 4. S cot63x dx de 5.55 sin

A:

Q: In (x) -dx is equal to x2 The numerical value of

A: Given is an integration and we have to find it's numerical value. Here, we use the Integration by…

Q: 16. S cot xdx /1 + In sin x

A:

Q: S tan* dx

A: Using , Trigonometry formula and integration rule

Q: S In(cos x) tan x dx

A:

Q: If y = -sin x, what x-value corresponds to a y-value of 1 between 0 and 27? [? ]T

A:

Q: Sy sinh dy a

A: