iii. Find the particular integral (P.I) of y" + 9y = cos 3x

Q: S,(4y³ +-) dy y3.

A:

Q: b) Calculate the following integrals x²(3x³ + 2)²dx (i) (ii) sin3x e³x dx (ii) (2x22+₁ +*²+2) dx S…

A:

Q: |(x² + 2x) cos(2x) dx

A:

Q: Q3/ Evaluate the integral: TT ° cos(x²)dx dy

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 1. Compute the following integrals. (a) dx. (b) 2° sin(x³) dx.

A:

Q: Determine the fool wing integrals: 1. e2*cos3xdx . 2. J.x² In(x+ 4) dx -

A: Use integration by parts

Q: I. Evaluate the following integrals. 1. Sx sin 3x? dx tan y 2. S dy 1-tan²y 3. S sec?(3 – 2t)dt

A:

Q: Evaluate the integrals in ∫2ey cos ey dv

A:

Q: Q2 (a) Calculate each of the following integrals. sin 3 0 cos'e 1 S sin x(cosx)4 dx

A:

Q: The particular Integral for (D2 + 42)y = sin4x is. Yp

A:

Q: Q2/ Find the value of the following integrals: 1- |((x+y)dx + (y – x)dy), when cis given by, x = cos…

A: The integrals in the form ∫C(x+y)dx+(y-x)dy involve the integration over a particular curve C. In…

Q: what is the integral of e^(-2a|t|) from 0 to w

A: Given integral: ∫0we-2atdt

Q: Evaluate the integrals ∫cos (1 - ln y)/y dy

A: We have to find the integrals: ∫cos1-lnyydy We will find this integrals by substitution method Let…

Q: 1. Evaluate the iterated integral: r12 Jo o cos(2) dy dx. -

A: To find ∫π2π∫0x21xcosyxdydx: First solve ∫0x21xcosyxdy: Let u=yx  dudy=1xdy=xdu…

Q: Q1. Evaluate the following Integrals 1 dx 1- cos x .2 +x - 2x +3 dx

A:

Q: dx e2a +5

A:

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: 1. Compute the following integrals. (a) sin (e) dx. 4 dx. - (b) x2

A: we have to calculate integration

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: Find the approximations   T 8  and    M 8    for the integral integral 0 to 1 cos (x 2   ) dx

A: Given ∫01cos(x2)dx

Q: 1. Evaluate the following integrals. ? cos(r) dt а. Зx2 — 1 dx b.

A:

Q: Which of these is a non-elementary integral?" ( In(2y² + 1) -dy 4y A. * cosh(2x) xp. B. +…

A: (a) For, Is non elementary since y is in denominator. (b) For Is non elementary since x is in…

Q: Find the integral. e4X cos 3x dx + C

A:

Q: Q. No.5 Compute the integrals: a) S* 4 sin* x cos?dx b) , cos 2y sin 5y dy

A: Given:  5. a) ∫0π4sin4x cos2x dx b) ∫-π0cos2y sin5y dy

Q: Sin (x-t) u(t) dt = 1- Cos x

A:

Q: (a) Evaluate the following integrals: π cos(x) dx dy 4y

A:

Q: Evaluate the integral. integral  cos 3x e x dx

A:

Q: 1. Evaluate the integral: (a) cos(x) dx dy 4y

A: the given integral is: we have to evaluate the given integral.

Q: Evaluate the integral. T/2 9 sin2(x) cos2(x) dx

A:

Q: 1. Compute the following integrals. (a) dx. (b) x³ sin(æ³) dx.

A: We have to integrate both

Q: Q1)Evaluate the following integral: Sz cos . sin dx 2 2

A:

Q: Determine the following particular integrals: -{3x²e-x} 2.1 2.2 1 D² + D-1 1 D² - D+2 {8 sin x cos…

A: To Determine: the following particular integrals:   2.1 1D2+D-13 x2 e-x 2.2  1D2-D+28 sinx cosx

Q: Evaluate the integral. * T/2 sin³x cos y dx

A: Using identity         Sin2x+cos2x=1

Q: 1. Evaluate the integral. S. a) t sin3tdt b) / V1+a* dx

A: (a) Given: ∫0πt sin 3t dt Apply integration By part : ∫I.II dx=I∫II dx-∫ddxI∫II dxdx Take: I=t and…

Q: Evaluate the multiple integral cos(x - y) dx dy

A: Here we have, I=∫11+π2∫1ycosx-ydxdy

Q: Which of the following is not an improper integral? cos x dx cos x dx 1 dx cos x 1 dx cos x 8.

A:

Q: ...... ... ... ...- Evaluate the iterated integral. 5. y cos(x) dy dx

A:

Q: 9/u The evaluation of the Integral of S° sin2x cos4x dx is

A: we have to integrate

Q: Evaluate the integrals ∫cos t/1 - sin t dt

A: Given :           ∫cos t1-sin tdt

Q: Evaluate the integral of sin 6 (x) dx from 0 to Tt/2. * 5п/32 2n/17 T/32 3Tt/32

A: Given: The objective is to integrate the function sin6(x)dx from 0 to π2.

Q: Which of the following is not an improper integral? 1 dx cos x 2 cos x dx | cos x dx 0. 1 dx cos x 2…

A: Given, The definite integrals We have to find the integral which is not improper.

Q: Evaluate the integral / 'cos(æ – In x) dx dy.

A: We need to change the order of double integral

Q: 10. Find the indefinite integral. Te cos 3t dt dv u = du = v =

A: Given integration is : ∫e9tcos3t dt   To find the value of integration.

Q: Evaluate the given Integral 1. ſ csc x (cos2 x - 1)dx

A:

Q: Evaluate the double integral: cos(y') Vy3 dy dx.

A: The solution is given as

Q: 2.2 Evaluate following integrals. .sin VT cos E 2.2.1 dx

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: Evaluate the integral. Tt/3 V1 + cos(2x) dx

A:

Q: 11. Evaluate the definite integral S" dx. x+a?

A: Topic:- definite integration