7. Find the indefinite integral. (a) + sec , | dx = 4 In |x| + tan(x) +C (b) / )Lanr dx = In |In x| +C x In x xt – 3x² + 5' (c) 3 dx = x+ 3r3 +C

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: Evaluate the integral. 3 1 3y2 cos xy dy dx x/3 5(1 - cos 3) 3(1 - cos 3) cos 3 - 1 (1 - cos 3)

A: Formulae used: ddxxn=nxn-1∫cos(ax)dx=sin(ax)a+C∫sin(x)dx=-cos(x)+Csin(0)=0cos(0)=1

Q: 8. Find the general indefinite integral (x³ -2² + x)dr; b) / (2" +-)dr, x > 0; c) (sin(3t) +…

A:

Q: 3. Find the following definite integrals. (2x +3)dx (x2- 1)dx x² - 2x)dx sin(3x + 4) dx 1

A:

Q: Evaluate the integral: e³+cosh2x33+cosh2xsinh2x dx A (3e)3+ sinh2x 2In3 + C (3e)3+ sinh2x B 2 + In3…

A:

Q: 6. The improper integral dx converges to /x- 5 '5 Vr-5

A: The given integral is an improper integral of second kind.

Q: 4 18. Evaluate the indefinite integral / dx. 3 X,

A: Given integral to find ∫4x3dx To integrate this first take the constant out 4∫1x3dx Applying the…

Q: 6. Evaluate the integral ex e* +e-xdx

A:

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

A:

Q: n x³cos²x dx Compute the integral. -T 1+sin10x

A:

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

A: Given,

Q: 13. Evaluate the indefinite integral fx cos x dx x sin 2x cos 2x a. + c 2 x sin 2x cos 4x b. + c 2 2…

A:

Q: 3. Evaluate the double integral /sin(x+y) dx dy by using Simpson's 1/3-rule with four sub-intervals.

A: I = ∫0π2∫0π2sin x+ydxdy,

Q: 7. Which of these is a non-elementary integral? In(2y² + 1) А. -dy 4y e-x cosh(2x) В. c. [ e-x +…

A: Non-elementary integral for a given elementary function is an  indefinite integral that is, itself,…

Q: How do I calculate the indefinate integral of e^sinx(cos(x))dx

A: Given integral is ∫esinxcosxdx

Q: =dx V2x* +3 4

A:

Q: 2. Find the indefinite integral: S (Vã+ - x + - 1) dx 6 .3 X X

A:

Q: integrals in Erarnices 6 to 20: dx 8. (ax +bx+c) dx 7. Vx - 1 dx (11 x' +5x - 4 dx dx 10. - dx…

A: Given :

Q: 1) Evaluate the integrals: (a) f sin³ (2x) cos (2x) dx (b) sin³ (2x) cos (2x) dx

A:

Q: Consider the improper integral: x² +2x+2 dx what will be the appropriate solution and answer? A Im…

A: ∫0∞1x2+2x+2dx

Q: 5. Find the indefinite integral. A) f dx (x-3)Vx -6x+5

A:

Q: 3 9-x 9-x2 Evaluate the integral dz dy dx. 0 0 . 0

A:

Q: 7 In x (1) Evaluate the definite integral dx.

A:

Q: 22. Detemine whether the improper integral converges or diverges, and if it converges, find its…

A:

Q: (6) Find the indefinite integral (af* -3x +2 Fdx x+1 12x - 22x (bJ -dx 3x* -11x +15 x² + 2x +3 -dx…

A: Note: As per companys policy we should do maximum 3 subparts of a question.So, kindly post the other…

Q: 5 Only one of these calculations is correct to evaluate the definite integral 7x In(x) dx Using the…

A:

Q: 4. Evaluate the improper integral. dx х2 — 1

A: Consider the given integral as Solving the integral

Q: 13. Find the integral using the u substitution method Jx(x+1)*dx

A: Solution of question as follow

Q: Show that integral 0 to infinity  x2 e -x2  dx = 1/2 integral 0 to infinity e -x2  dx

A:

Q: 7 If the change of variables u = x-1 is used to evaluate the definite integral f(x) dx, what are the…

A: This question can be solved using the concept of change of limits in definite integrals.

Q: 4. Determine the following integrals 4.2 - dx - a x

A:

Q: 2. Use integration by parts to establish the reduction formula: Sx" cos x dx = x" sin x – n x"-1 sin…

A:

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: Step by step

A:

Q: - Prove using integrals Proper tos : e even sin()fc) dx=0 -b 9- For even functions.

A:

Q: Find the indefinite integral. (a) / (2* + v#)dx (c) / 2x6 + x5 -dx x4 (4) [(4cs (xỉ + 5x + 4)dx (4…

A: Note: As per our company guidelines we are supposed to answer the first three sub-parts of the…

Q: 4. Determine the following indefinite integrals: a) S(2x* + 3x³3 – 7x² + x – 5) dx b) S(x – 5)² dx •…

A: 4. Power rule of integration states that: ∫xndx=xn+1n+1 (a)To evaluate the integral:…

Q: 5. Find the particular integral of d²y + dy - x2 + 2x + 4 dx2 dx

A: We use the operator method to find the particular integral of the given differential equation.

Q: Evaluate the integral: e3+ cosh2x33 + cosh2xsinh2x dx A (3e)3+ sinh2x 21n3 +C B (3e)3+cosh2x 2+2ln3…

A: This question can be solved using integration by substitution.

Q: how do I find the integral of e^-xsec^2(e^-x)dx

A:

Q: 3. Estimate the integral v2 + x² dx using appropriate of Simpson's rule with step size, h = 0.2.

A:

Q: 2 1. Evaluate the integral: dx 2 x2-x

A:

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

A:

Q: 5. Evaluate the definite integral (1+lnx)² dx а. 1 dx. b. -1 2x+3

A: Explanation of the answer is as follows

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: 1) Find the indefinite integral S(3x* – 6vx + 3 cos x – 4e*)dx. 2) Find S 4(sin(6 sin x + x² + Vx))…

A:

Q: 1. Evaluate the integrals that converge: dx 2x ! dx (x2 + 5)3 b) a) 3-x - 00

A:

Q: (6) Find the indefinite integral - 3x+2 x+1 12x-22x dx (O) 3x -11x +15 x' +2x +3 dx (c)+3x +9x x In…

A: Solution is given as below: