a) Evaluate the integrals using appropriate substitutions. Sine ii) S - de Cos20+1

Q: 10. Prove by using integration by change in variable the ff. integral: dx :du 3D arcsecх+ С xVx2 – 1

A: We have given the integral ∫dxxx2-1 = I(say)     Put   x2-1 = t   ⇒x2= t2+1     Differentiate w.r.t…

Q: Use the tabular method to evaluate the integral - 2x – 1) cos(4x)dx

A: Introduction: Tabular integration is a technique for quickly integrating many parts in a row. One of…

Q: Use any method to evaluate the integrals ∫cot x/cos2 x dx

A:

Q: (b) Evaluate the integral using by parts (* sin 2xdx formula:

A: Let I=∫x2sin2xdx. We have to evaluate the integral by using integration by parts.

Q: Evaluate the integrals ∫sin 5u cos 6u du

A:

Q: x arcsin(x²) dx;

A: Given that: *∫sin-1u×du=u×sin-1u+1-u2+C The given expression is, ∫x×sin-1x2×dx Let,  x2=u,…

Q: (a) Evaluate the integral | 16х -dx by using substitution. 8x +2 (b) Evaluate the integral using by…

A:

Q: Evaluate the integrals. It may be necessary to use a substitution first. ∫ sin θ dθ/cos 2θ + cos θ -…

A:

Q: calculate the integral: Integral[0, pi/2] 24x^3sin(x)dx

A:

Q: Use the Table of Integrals to evaluate the integral. (Use C for the constant of integration.)…

A: Given,            ∫sin2θ8-3sinθdθ

Q: 1. Jx cos 3x dx

A: Question 1 is solved. Solving more than 1 is against the policy.

Q: I sin³x 5 sin x 4 cos x dx

A: To find out the integration.

Q: Use the table of integrals to evaluate the integral. (Use C for the constant of integration.)…

A:

Q: use an appropriate substitution and then a trigonometric substitution to evaluate the integrals.

A:

Q: Evaluate the integral / 8 cos (x) sin(2x) dx Note: Use an upper-case "C" for the constant of…

A:

Q: Evaluate the integral: CT/2 cos² (4x) sin³ (4x) dx.

A:

Q: 1 x² cos(x³) dx CoS

A:

Q: Evaluate the integral using the methods covered in the text so far:                    ∫ cos x5−2…

A: I=∫cosx5-2sinxdx Let us suppose -2sinx=t, then Differentiating to both the sides w.r.t x-…

Q: 4. Evaluate the integral sin x cos x dx by two methods: first by letting u = sinx, and then by…

A:

Q: dx so that the resulting integral is integrable? What should be the rewrite of the integrand of…

A:

Q: Use the table of integrals to evaluate the integral. (Use C for the constant of integration.)…

A: The given intregration,∫sin2θ3-7sinθdθ

Q: 10. Prove by using integration by change in variable the ff. integral: dx du = arcsec x + C xVx2 - 1

A: To show∫dxxx2-1=sec-1x+C.

Q: What is the integral of 10pi(4-y)(sqrt(siny))dy from 0 to pi?

A: Let I=∫0π10π4-ysinydy Then, ∫0π10π4-ysiny…

Q: Ssin( /3x)cos(-2r)dx

A:

Q: a) Evaluate the integrals using appropriate substitutions. Sine ii) S de Cos0+1

A:

Q: Evaluate the integral using trigonometric substitution with x = 2 sin(0), x = 2 tan(0), or x = 2…

A: From the given problem:   I=∫ x34-x2dx ....(1)   Now substitute these values in equation(1).…

Q: use an appropriate substitution and then a trigonometric substitution to evaluate the integrals.

A: Evaluate: ∫1-(lnx)2xlnxdx

Q: Evaluate the integral.

A: Given ∫0π2sinθ·ecosθdθ

Q: Evaluate the integral. A/2 sin!'(0) cos (0) de COS Jo

A: Given : ∫0π2sin11(θ)cos5(θ)dθ ∫0π2sin10(θ)sin(θ)cos5(θ)dθ∫0π2sin2(θ)5sin(θ)cos5(θ)dθwe know that…

Q: sin2t costdt

A:

Q: Evaluate the integral using trigonometric substitution with x = 2 sin(0), x = 2 tan(0), or x = 2…

A:

Q: 8. Evaluate the integral by using trigonometric substitution 2 dx V4x – x2

A: We have to find the indefinite integral.

Q: Compute the indefinate integral. integral (1-sin^2(x))/cosx * dx

A: Consider the given integral.

Q: Use the Table of Integrals on Reference Pages 6–10 toevaluate the integral. integral     sin 6 2 x…

A: Consider the given:∫sin62x dx Apply u-substitution:  2x=u∫sin62x dx =∫sin6u12du=12·∫sin6udu

Q: (b) 3 – cos(x) 2

A: Follow the procedure given below.

Q: evaluate the indefinite integral.

A:

Q: Evaluate the indefinite integral: (3e" + 6 sec? u) du: |+ C.

A: As per guide line we have

Q: 4. Prove using the results concerning iterated integrals that In 5 dx = 4 sin? x

A: Given:-                 To prove the result concerning iterated integrals that…

Q: evaluate the integral using the methods covered in the text so far.

A:

Q: dt cos°(2 sin" 21)/1– 4r cos(2 sin2t

A:

Q: Use a table of integrals to find the indefinite integral ∫ θ3 /(1 + sin θ4) dθ

A: To Determine: use a table of integrals to find the indefinite integral Given: we have ∫x31+sinx4dx…

Q: Compute the defined integral So [1+ e* sin(4x)] dx using the trapezoidal method with two segments.…

A:

Q: Use the Table of Integrals on the Reference Pages toevaluate the integral.

A: ∫cosx4+sin2x dx Put, sinx=t⇒cosx=dtdx⇒cosx dx=dt

Q: To evaluate the integral dz, we use Select one: Substitution with z = 2 sin 0, where 2 O…

A:

Q: (n) /* dx sin? 4

A:

Q: 5. cot x cos²x dx In

A: We will evaluate the given integral as shown below

Q: The area under one arch of y=sin(0.5x) is O 0.2 O 0.5 O 0.8 None of them

A: Given: y=sin(0.5x)

Q: Use the table of integrals to evaluate the integral. (Use C for the constant of integration.) 9 sec²…

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

Q: Evaluate the integral. (Use C for the constant of integration.) integral of 2 cos(θ)…

A: To determine the value of the integral.