Рл/6 sin 2x cos 4x dx 61.

Q: S(sin5 2x) (cos 2x)dx

A: To solve this integral, a certain substitution is done. The substitution of sin2x=u is taken and…

Q: Use a table of integrals to find the indefinite integral.

A: Integration is summation of discrete data. The integral is calculated for the functions to find…

Q: Evaluate the definite integral 3 10 sin (z)dz

A: To solve the definite integral. Ans=5

Q: Evaluate the following integrals sin³ (x) cos³(x) dx

A: Given ∫sin3xcos3xdx

Q: Evaluate the integral n/2 sin x cos x dx

A: This integral can be solved by the general formula of integration.   Integral ( 0 to Pi/2) sin^mx *…

Q: Evaluate the given integral. [ 2x?sin(4x)dx

A: The given problem is solved below in detail.

Q: Evaluate the definite integral: J 7 cos (2x + 7) dx Note: Round to the nearest tenth.

A:

Q: Find the indefinite integral. sin 60 V cos 60 de

A:

Q: V. S, sin* () cos5 (-) dx

A:

Q: 41 sin x cos x d

A: Given integral :

Q: Evaluate the integral. 17 sin?(x) cos (x) dx

A:

Q: Evaluate the integrals cos x dx 5. / sin x

A: since u have asked multiple questions in a single request so we will be answering only first…

Q: Evaluate the given integral. ∫ (x cos x + x sin x) dx.

A:

Q: 2. sin'0 cos e d0

A: We have to find the integral

Q: Evaluate the definite integral. 4 cos(πt/2) dt

A:

Q: Evaluate the definite integral. 7 cos(xt/2) dt

A:

Q: Use the Table of Integrals in the back cover of Stewart's text to evaluate the integral 2x sin(x?)…

A: We will use the formula here  2 sinA cosB = Sin(A+B)+Sin(A-B)

Q: Find the following indefinite integral: ∫ x1/3 sin(x4/3-8) dx

A: Given,            ∫ x13sin(x43-8)dx

Q: Evaluate the definite integral. Tt/14 cos(7x) sin(sin(7x)) dx

A: to find:- definite integral.

Q: Evaluate the given integral. ∫ (sin x - 3 cos x) dx.

A:

Q: cos° æ sin x dæ

A:

Q: Evaluate the definite integral. 1 6 cos(at/2) dt

A: Given:        ∫016cosπt2dt Taking constant out      =6∫01cosπt2dt substitute u=πt2…

Q: Evaluate the integral of (x^2)sin(x^2) dx as an exact answer.

A:

Q: Evaluate the integral. x sin(2x) dx = +C

A:

Q: Evaluate the integral. 7e" sin x dx +C

A:

Q: Evaluate the definite integral. cos(x)dx

A:

Q: Evaluate the following integrals.

A:

Q: Evaluate the following definite integrals sin 2x cos (sin x) dx

A: We know that2sinx cosx=sin2x

Q: Evaluate the integral. 2n x sin(x) cos(x) dx

A:

Q: Evaluate the definite integral. * T/2 9 cos(x) sin(sin(x)) dx

A:

Q: Evaluate the definite integral. 5 sin (z) cos(x)dx 0.

A: Given query is to find value of the integral.

Q: sin x cos(2x) dx

A:

Q: sin 2x dx .2. 1 + cos?x

A: Given, ∫sin2x1+cos2xdx   We have to evaluate the indefinite integral

Q: Evaluate the following integrals.

A: It is given that, ∫sin 2x lnsin x dxWe have to evaluate it.

Q: Evaluate the following definite integrals.

A: I =  ∫01xsinπx.dx  ................(1)we know ∫abf(x).dx = ∫abf(a+b-x).dx

Q: * sin'x de 4.

A:

Q: 1 dx sin°(2x)

A: Solution:Given∫1sin6 2xdxFormula;d uv=vu'-uv'v2sin2x+cos2x=1∫xn dx =xn+1n+1

Q: Evaluate the given integral or show that it diverges. =/2 cos xdx (1 – sin x)?/3

A:

Q: Evaluate the integral. sin(0) d0

A: This question is based on the concept of definite integrals . For integrating it first we have to…

Q: sin³ x cos² x dx

A: We have to evaluate the integral: ∫0π2sin3 x cos2 x dx Rewriting the integral, ∫0π2sin3 x cos2 x…

Q: Evaluate the definite integral. sin(4t)dt 0.

A:

Q: Evaluate the integral. 9e" sin x dx +C

A: We have to evaluate the integral ∫9ex sin x dx.

Q: sin*(x) cos²(x)dx 4 CO

A: To evaluate the integral ∫ sin4(x) cos2(x) dx

Q: Evaluate the integral sin(x²)dxdy.

A: This is a question from the double integral.

Q: Evaluate the integral. 14 sin (x) cos (x) de

A:

Q: Evaluate the following Integrals: 1. 6x² sin x³ dx

A: NOTE: As per our guidelines, I have solved the first problem in the picture.

Q: Evaluate the definite integral. cos(Tx) dx 0.

A:

Q: Evaluate the integrals ∫2 sinh (sin θ) cos θ dθ

A: Our Aim is to evaluate the integral given below:-I=∫2 sinh (sin θ) (cos θ) dθ -(i)

Q: Evaluate the integral.

A: Our Aim is to evaluate the integral given below:-∫cos (x)2+sin (x)dx-(i)

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.