The suitable substitution to evaluate the integral cos (2x) dx is csc (2x)

Q: 5) find the integral J8 sin 2x * cos2x dx

A: see below the calculation and answer

Q: Evaluate the indefinite integral; f Vtan 3x sec2 3x dx OA)-(2(tan [3x)^(3/2) ] /9 + C OB) I DON'T…

A:

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: Evaluate the definite integral. π/2 1- cos(2x) dx

A: Answer:-(1) Given the integral,     ∫sin2x cos22x dx=∫44*sin2x cos22x dx…

Q: Evaluate the integral. |cos 7x cos 3x dx

A: The given integral ∫cos7xcos3xdx.

Q: Evaluate the integrals ∫2(cos x)-1/2 sin x dx

A:

Q: Evaluate the integral: integral from 0 to Pi/2 of cos^3(x)*sin^(2/3)(x)dx

A:

Q: cos xdx x

A: The given integral is,∫xcosx dx. ∫xcosx dx=x∫cosx dx-∫ddx(x)cosx dx∫xcosx dx=xsinx-∫ddx(x)cosx…

Q: 5tan 2x -dx sin²2x-1 8.

A: Put tan2x=t and using integration of ax dx =ax /loga

Q: Use reduction formulas to evaluate the integrals ∫ 8 cos4 2πt dt

A: To solve,    ∫ 8 cos4 2πt dt Using reduction formula.

Q: Evaluate the integral. dx =, x>6 x - 36 dx x²x - 36

A:

Q: Evaluate the integral. ∫ x Cos 5x dx

A:

Q: dx 2+2 sinx + cos x

A: Given that the integral ∫dx2+2sinx+cosx. Evaluate the given integral. Formulae used:…

Q: Find the indefinite integral. |cos 2x ein 2* de sin 2x A) 2 +C ein 2x +C B) C) sin 2x e cos2x +C D)…

A:

Q: 1 x² cos(x³) dx CoS

A:

Q: Evaluate the integral. dx 9-x2 O sin-1 cos 1*+c O cos Cos 7 O 2 2 cos'1를x*C Sin 1

A: SOLUTION-

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: (1 if 0 1

A: The given function is,f(x)=1 if 0<x<10, if x>1

Q: Evaluate the integral ∫dx / 1+cos2x.

A: Recall cos2x = 2cos2x - 1 hence, 1 + cos2x = 2cos2x

Q: x° cos 2x dx

A:

Q: dx 2 sin x+3 cos x-5

A: Here we going to use some arrangements, look at the all steps carefully

Q: Evaluate the integral. integral  cos 3x  sin 2x dx

A:

Q: Evaluate the integral. integral 0  to pie /2     sin 3x  cos 2x dx

A: Consider,

Q: Ssin*(x)cos²(x)dx

A:

Q: dx x2-x

A: Convert the rational function into partial fraction. Use integration of 1/x dx = ln(x) +c

Q: Evaluate the integral ∫(cos x) esin x dx

A: Consider the following integral: ∫cosxesinxdx Substitute sinx=p→cosxdx=dp in the above integral:…

Q: Evaluate the integral 3 2x cos(xy)dydx 2

A:

Q: cos 3x cos 4x dx

A: ∫cos3xcos4xdx here we use formula  2cosxcosy = cos(x+y) +cos(x-y) here x = 4x      y = 3x

Q: Use the tabular method to evaluate the integral fa (x³ + 2x-1) cos(4x)dx COS

A:

Q: Find the indefinite integral. ∫cos3( x/3)   dx

A:

Q: Evaluate the integral/ cos'x sin x dx using the substitution u = cos x. cos"x sin x dx =

A: ∫cos11xsinxdx

Q: dx 1. -1 V1 – 2x – x²

A: Explained below

Q: the integral of tan^2x cos^3xdx

A: we have to find integral of tan^2xcos^3xwe use following rule

Q: cos (6x) cos (3x)dx

A: Solution :∫cos6xcos3xdxNote…

Q: Evaluate the integrals ∫cos x cos 7x dx

A: To integrate: ∫cosxcos7xdx.  We know that cosacosb=12sina+b-sina-b. Therefore, using the above…

Q: Evaluate the integrals ∫cos 3x cos 4x dx

A: Evaluate ∫ cos 3xcos 4xdx

Q: cos xdx 10. sin x

A: According to definition ∫f(x)dx=F(x), where dFdx=f(x).The function F(x) is called the antiderivative…

Q: Step by step

A:

Q: Find the indefinite integral.∫cos2 3x dx

A: To evaluate the indefinite integral ∫cos23x. Solution: The given integral is ,∫cos23x Multiply both…

Q: evaluate the Cauchy principal value of the given improper integral. cos 2r dx x² + 1

A: We have to find the Cauchy principal value of the improper integral. First we have to write the…

Q: Evaluate the integral of sin(4x) cos(3x) dx

A: We have to use 2sinAcosB= sin(A+B)+sin(A-B) formula to simplify first.

Q: Evaluate the integral. ∫x  Cos2 x dx

A: Given- ∫xcos2x dx To Find- The value of the above integral. Identity Used- cos2x=1+cos2x2

Q: Evaluate the integral ( sin(In(2+2x)) x+1 dx

A: Given: ∫sinln2+2xx+1dx

Q: Evaluate the integral.

A: Our Aim is to evaluate the integral given below:-I=1[cos(x)-1]dx     -(i)

Q: Evaluate the integrals ∫cos2 x dx

A: Given:∫cos2 x dx

Q: x cos 5x dx

A: The integral is evaluated in detail below.

Q: Evaluate the integral

A: The given integral is: ∫3x1-cosxdx To evaluate this integral, consider x=t  .......(1). On…

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.