Exercise 2: Solve the following integrals. (a) / sin" (x) dx (b) / a | cos (x) sin (r) dx .4 3 (c) / sin (x) cos (x) dx (d) / sin (x) cos° (x) dx 18

Q: b,c,d

A: (b) The given integral is

Q: 1. Solve the following integral by using the Integration by Parts. (a) x sin x dx (b) e 2x sin 2x dx

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Q: 3., J(5 cos x+4 sin x) dx

A: We have to find integration

Q: 1 Use the integration formula ax dx = ax + C to find 4* dx and simplify. In(

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Q: B) Use the techniques of integration to evaluate. (Solve 2 only) 3) J tan-ty dy dx 2) (1– x²)5

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

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Q: Use MUPAD to determine the following indefinite integrals (7.1) (7.2) (2ax-x²)³ dx. S (7.3) Obtain a…

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Q: If you are asked to find the indefinite integral of f(x) = x ln(x), and you are told to integrate by…

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Q: Q4: Solve the following integrals:- dx ³-2x² (1) dx (2) √ √2√9-1² (3) fx² sinxdx (cos-14x)² 1-16x²…

A: Since, you have posted multiple questions, as per guidelines, we"ll solve only first three…

Q: Q: Find the integration for the following functions: - 1.- °(1-cos2x) 2-5 2- sin(tnx) dx 3-f-…

A: According to the guidelines issued by the company we are supposed to answer only first three sub…

Q: Find the indefinite integral.

A: Let ex+e-x=v. Differentiate both sides: (ex-e-x)dx=dv Substitute v and dv in the integral…

Q: (a) Define a substitution variable u and write / x(x +1)*dx in terms of u. Do not solve the…

A: detailed solution is given below

Q: (sec2 x + csc2 x)cos2 x dx

A: Given: I=∫sec2x+csc2xcos2xdx   Use the trigonometric identity; 1). sinx=1cscx 2). cosx=1secx And…

Q: Q4: Solve the following integrals:- dx 4dx (1) f 2+cos x (2) J sec xesin x (3) Sx sec? x dx dx (4) )…

A: Indefinite Integration

Q: se C for the constant oT integration.) (7 cos x + 3 sin x) dx

A:

Q: Solve the integral equation F(x) cos px dx =. [1-p,0sp 1.

A: Since you have asked multiple questions, we will answer the first question. If you need answer for…

Q: Evaluate the integrals sin2.x -dp- J(5 + cos2.x) e) 3

A: Since, you have asked multiple question, we will solved the first question for you. If you want any…

Q: What is the integral of ((x^2)*e^(3x))dx from 0 to 1?

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Q: Choose the most appropriate answer: Evaluate the integral : J(e- 182 + sin 11x) dx -18x e + cosll +C…

A: We need to evaluate the following integral : ∫e-18x + sin11xdx

Q: Q2 Find the integral for the following : dx 1 1-5 2- fe-*sec? (ne-*)dx 3- S dx 2vx+2x 1+e*

A: We have to find the Integral for given expressions. 1. ∫dx/(2√x + 2x)  2. ∫e-x sec2(πe-x)dx  3.…

Q: Evaluate the integral. 1 (x² + 3)e¯× dx 0.

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Q: The integral of the given function | cos(9x) cos(5x)dx is equal

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Q: J cos(2x)e2x dx (recurring)

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Q: For the following integration / sin"(24x) cos(24x)dx what is the suitable substitution? a.…

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Q: In the integration of (cos y)^2 dy/(1- sin y), what is the first step to solve the integral? *

A: Given,          ∫cosy2dy1-siny

Q: f1-p, 01 Solve the integral equation F(x) cos px dx Hence deduce that Sin dt 2

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Q: What is the particular integral of the equation (D 2+9) y= x Cosx?

A: Use basic properties and formula, get PI of given equation.

Q: Q4: Solve the following integrals:- dx 4dx dx (1) S: (2) S sec xesin x (3) S x sec? x dx (4) S -…

A:

Q: Q1: Verify that the given functions are solutions of the corresponding integral equations by using…

A: Given: ₵(x)=xex and ₵(x)=exsinx+2∫0xcos(x-t)₵(t) dt

Q: Q1: Evaluate the following Integration: a) ( In(x²+x)-Inx-en3 dx b) S; sinx Ine(x+1) 1-cos²x

A: Answer (a): To evaluate this integral, apply the logarithmic properties : And, And, And, And,…

Q: Solve the integral: dy dx. x2 H/4

A: To solve: The integral ∫141∫x2xxydydx. Formula used: ∫xndx=xn+1n+1+C Here, C is constant of…

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

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Q: Q3/A) Evaluate the integrals S sin(ln x)dx

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Q: 4. Evaluate the following real-variable integrals using the method of residues: 2 cos (0) Jo…

A: PART A Consider ∫02πcos2θsinθ+2dθ Let us assume : dz=eiθi dθdz=iz dθdziz=dθ

Q: I. Evaluate the following integrals. 3.x5 dx V2 – x3 1. - 2* + e2" sin(2") dx sin(2") 2. 2x + 3 dx…

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Q: Q1) A: Solve the differential equation: x- y = x.cos? ? dx B: Evaluate the following integral by…

A: Follow next step

Q: dx (b) . +2) (x +3)

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Q: Solve the integral equation f(x) cos Ax dx = e. %3D

A: Given integral is, ∫0∞fxcosλxdx=e-λ The right-hand side is a Fourier cosine transformation function…

Q: Find the indefinite integral x2e +e² dx.

A: The given indefinite integral is: I=∫x2e+ex dx

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: Solve the integral equation F(x) cos px dx: [1-p, 0sps1 0, p > 1.

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Q: (a) Solve the following integrals. (i) (ii) x' + 3x? – 10 - dx x(x – 3)(x+1) Integrate er* cos (3x)…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: (d) L™ x³ cos(x* + 5) dx. (e) f(2x – 1)³ dx . -

A: For the given integral  ∫0π4x3cos(x4+π2) dx

Q: Change the order of integration. "A/2 x + 1 3 sin(x) dy dx

A: Consider the graph:

Q: dy y(y²+1)

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Q: Evaluate the following indefinite integrals. Show your solution. 1. f5 einx(sin x + cos x) dx ecos…

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Q: a) Solve the integration by parts [cos(x)e*dx.

A: We need to solve the given integral  This can be evaluated as follows:

Q: Q4: Solve the following integrals:- 4dx dx (1) S: (2) S sec xesin x (3) S x sec² x dx dx (4) J 2+3x…

A: Using definite integral

Q: dx 1. S (2-3x)2 2. S V2x + 1 dx

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Q: Q.4 Use the integration by parts to evaluate the integral. V3 2 sin-1 x dx

A: