5. Evaluate the integral. 8 sec* x dx 8(sec x + tan x) + c tan' x+C O A tan x+C t an² x + C 8 tan x + OD.

Q: 3. Find the integral (a) f(cos(x) + sin(x))² cos(2x) dx 1/3 /tan(x) (b) dx sin(2x) tan-¹(x) dx (d)…

A: (a)  I=∫cosx+sinx2cos(2x)dx =∫(cos2x+sin2x+2sinxcosx)cos(2x)dx =∫(1+sin2x)cos(2x)dxHere, Let…

Q: A. Evaluate the following integrals. 1. S(Vcos x + sin x)´dx 2. S cos³ 3x dx 3. S tan5 2x dx

A: To evaluate the following integrals.1 ∫cos x+sin x2 dx2 ∫cos33x dx3 ∫tan52x dx

Q: 12. The integral of dy S Sec-' (5 ) + C 3 O ţSec-"' ( ) + C 3 Sin-l (플) G) +c 3 o Sim' (등) +C O…

A: This is based on simple formula of integration

Q: 13. Consider the integral | dx then (which statement(s) is/are correct) x2 - 4x 1 (i) -dx…

A: Given: ∫1x2-4xdx

Q: Evaluate the following integrals: 1. S(cos x + csc² x)dx 2. S(tan x + sec² x)dx 3. S(1+sec²x)dx 4.…

A:

Q: 1. Compute the following integrals. 1 cos 3x dx b) VAr + 7 c) a) dx dx sin x / (In x)3 f) / d) ſ eª…

A:

Q: 7/2 2. Is cot x dx an improper integral? Explain.

A: Given integral is not an improper integral.

Q: 2. Evaluate the improper integral. e COs x dx

A: I=∫0∞ e-x cosx dx Integration by parts;Formula:∫(uv)dx=u∫vdx -∫dudx ∫vdx dxu=cos x, dudx=-sin…

Q: 3. Find the indefinite integrals. (a) /4 dx (b) /2* r 2x-x2 dx

A: Given two functions integrate it by use of formulae

Q: dr

A: Given integration is : ∫x2-9x3dx To find the value of integration.

Q: 1 Evaluate the improper integral dx. (x – 3)3/2' 3 -

A:

Q: 17. Evaluate the indefinite integrals. a) sin x cos x dx x +4 b) S dx (x2 + 8x- 7)2 c) S sin x dx…

A:

Q: Evaluate the integral.   ∫0 1 (x2 +1) e-x dx

A: Evaluate the integral.   ∫0 1 (x2 +1) e-x dx

Q: Solve the problem. Integrate f(x, y) = sin(x2 + y2) over the region 0<x2 +y2< 100. O T(1 - cos 100)…

A:

Q: 3. Find the indefinite integral: Sx(x-2)* dx

A: Please rate

Q: 3. Evaluate the indefinite integral 1 -dx x' + 3x? 3

A: Given,

Q: (5) Evaluate the indefinite integral (a)f(e* +3x² - sin x )d&x – sin x dx (b)|(secx tan x+cos x)dx…

A: We are authorized to solve only 1 question with 3 subparts please repost remaining parts Indefinite…

Q: 19. Evaluate the integral Z √(x^2 − 9) / x^3 dx

A: firstly divide the numerator by denominator part by part to simplify the integration

Q: Evaluate the iterated double integral √1-x² _L [ ³²-x² sin (x² + y²) dz dy dx

A:

Q: 5. Evaluate the following integrals: sin x (1) f dx (ii) [Vsinx cos xdx (iii) -x' dx x* +3x? +2 V1+…

A: Dear student,                      According to our guidelines we are supposed to answer only first…

Q: +00 dx II. Evaluate the improper integral x(In x)²

A:

Q: 3 Which of the following is equal to / sec 2 x tan³x dx to obtain the correct indefinite integral? A…

A:

Q: The improper integral e-3x dx 0. equals Refer: improper integral O 1 O 1/3

A:

Q: 0; x 0

A:

Q: 5. Evaluate the integral: Jsin?x cos'x dx

A:

Q: Q2:A/ Evaluate the integrals sec (1 + ex) tan (1 + e'/x) dx

A: Integral

Q: II. Evaluate the following integrals: 7 ax 52X+7 13. [ sin x 2 - cosX (1x dx 14. S MA sec² 3x -dx 1…

A:

Q: Evaluate the integral T/3 4 3 tan (x) sec*(x) dx

A: SOLUTION-

Q: 3. a. b. Evaluate the following integrals 2dx dx cos²x√4 tanx - tan² x sin(√x)dx J I sin

A:

Q: dx integralini hesaplayınız. x(In x)

A: Fundamental theorem allows us to compute definite integrals using the antiderivatives. It states…

Q: 7. Find the indefinite integral. (a) + sec , | dx = 4 In |x| + tan(x) +C (b) / )Lanr dx = In |In x|…

A: Given that: (a)∫4x+sec2xdx(b)∫1xlnxdx(c)∫x4-3x2+5x4dx

Q: 15 Find the integral | 2/x (1+x) dx.

A:

Q: Evaluate the integral (i) S 3x3 sin 4x dx (ii) S In (x³ + x) dx

A: This section looks at Integration by Parts (Calculus). From the product rule, we can obtain the…

Q: Q2:A/ Evaluate the integrals 1/x sec (1 + e) tan (1 + e) dx Q2:B/ Find dy/dx Vidt sin x cos t dt 2

A:

Q: 2. What is the integral of (2sec² x - sin x) dx? A. 2 cos x + tan x + C B. C. 2 sin x + cos x + C D.…

A: Using the sum rule, it can be written that ∫fx±gxdx=∫fxdx±∫gxdx. If ddxF(x)=f(x), then…

Q: 6. Which substitution can work to compute for the indefinite integral fx√√x + 5dx? A. u=x C. u=x+5…

A: we use substitution method to  find the value of integral

Q: Evaluate the integral (i) S3x3 sin 4x dx (ii) ſ In (x³ + x) dx (ii) cot-1 2x dx (iv) ſeax cos bx dx

A:

Q: a) [ ]: Evaluate the integral (4x + 1) In x dx c) [ ]: Evaluate the integral 2 dx (x – 1)(x + 4) |

A:

Q: Consider the improper integral dx . What is the appropriate solution and answer x2 + 2x +2 A lim…

A: We can solve given problem as follows

Q: السؤال 8 Evaluate the improper integral if it exists e'dx: - 00 -e.1 O e.2 O .3 0 The improper…

A: We will evaluate the integral and check if it converges.

Q: We want to compute the integral tan e dx. If we use integration by parts, with u(x)=tan-lr and…

A:

Q: 3. Find the value(s) of c that satisfies the MVT for Integrals 4 sec x tan xdx

A:

Q: 1) Evaluate. Јx cosh ax dx 2) Evaluate the integral. (In x)² dx x3 1

A:

Q: a) [ „J: Evaluate the integral (4x + 1) In x dx b) ' . Evaluate the integral fou 6 tan' x sec* x dx…

A: a) Given:       ∫4x+1ln x dx Integrate by parts: ∫fg'=fg-∫f'g where f=ln x , g'=4x+1           f'=1x…

Q: 3 1 dx :-1 Evaluate the improper integral: X -

A: ∫031x-1dxlet u = x-1dudx = 1→ du = dx= ∫031udu= ln(u)03

Q: 13. Evaluate the integral dx x – 1

A:

Q: 15. Evaluate the integral 10 ·dx (x – 1)(x² + 9)

A:

Q: 46) Estimate the minimum number of subintervals needed to approximate the integral T/2 6 sin x dx…

A: Find the minimum number of Subintervals.

Q: Answer 1 only. Upvote if it is typewritten.

A: We have to find the integral