– 16 dx x2 -

Q: Find the indefinite integral. (Use C for the constant of integration.) V tan(8x) sec?(8x) dx

A: We will use the substitution, tan(8x) = u³ and proceed as follows :

Q: Find the indefinite integral using the substitution x = 8 tan(0). (Use C for the constant of…

A: to find:- integral value of the given function.

Q: Find the indefinite integral. (Use C for the constant of integration.) secó 4x tan 4x dx

A: Use substitution tan(4x)=t

Q: Find the indefinite integral. (Use C for the constant of integration.) 3 sin 3x dx

A: The integral is ∫ 3sin3xdx By using the constant-multiple rule, ∫ c f(x) dx =c∫f(x) dx Here c = 3 ∫…

Q: up 1. √ √2x + 1 dx

A: The given integral is ∫042x+1dx. We have to evaluate the integral.   As per guideline, we have to…

Q: Find the indefinite integral using the substitution x = 3 sin(0). (Use C for the constant of…

A:

Q: r" (tan (x)) (In (cos(x))) dx

A: solve this integration by substitution. substitue                    ln(cos(x)) = t on solving

Q: Evaluate the definite integral using (a) the given integration limits and (b) the limits obtained by…

A:

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

A:

Q: Evaluate the integral. (Use C for the constant of integration.) 1 - 4x2 dx

A: Given that∫ 1-4x2 dxwe need to evaluate it

Q: Use the Special Integration Formulas to find the indefinite integral. ∫ √(36 − 5x2 )dx

A:

Q: Find the indefinite integral by using the substitution x = 4 tan(0). (Use C for the constant of…

A: The integral is ∫4x2(16+x2)2dx Substitute x=4tan(θ) ⇒dx=4sec2θdθ…

Q: (1 – x²) dæ Using appropriate trigonometric substitution then changing the limit of integration, the…

A:

Q: Find the indefinite integral. (Use C for the constant of integration.) (sin(x) – 4 cos(x)) dx

A:

Q: Find the indefinite integral. (Use C for the constant of integration.) sin 4x sin 3x dx

A: We know sin A·sin B=12cos(A-B)-cos(A+B) ∫cos ax dx=sin axa+C  where C is constant of integration.

Q: Find the indefinite integral. (Use C for the constant of integration.) tan' x dx sec10 x

A:

Q: Evaluate the integral. (Use C for the constant of integration.) 8x2 dx

A: Explanation of the solution is given below....

Q: Find the indefinite integral. (Use C for the constant of integration.) sin 3x sin 2x dx

A:

Q: Use a table of integrals to evaluate the definite integral.

A: Given: I=∫0π2xsin2xdx for evaluating given integral, we use integral by parts theorem according to…

Q: Find the indefinite integral using the substitution x = 6 sec(o). (Use C for the constar…

A:

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) (4). 1 sin dx

A: Indefinite integral

Q: Find the integral involving secant and tangent. (Use C for the constant of integration.) sec 4x dx

A: From the given information. The objective is to calculate the integral of the following.

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) COS X dx (sin x)20

A: Given, ∫cosxsinx20dx We have to evaluate the indefinite integral.

Q: Evaluate the integral. (Use C for the constant of integration.) fu- (x – 3)sin(Tx) dx

A:

Q: Evaluate the indefinite integral. (Use C for the constant of integration. sin(2x) sin(cos(2x)) dx

A: To evluate: I=∫sin(2x) sin(cos(2x)) dx...(1)

Q: Find the integral. (Use C for the constant of integration.) (x6 + 5-×) dx

A: In this question, we need to find the integral of given function.

Q: Find the indefinite integral by using the substitution x = 6 tan(0). (Use C for the constant of…

A: The solution for the above question is as shown below.

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) cos(x) sin20(x) dx

A:

Q: Use the table of integrals to evaluate the integral. (Use C for the constant of integration.) [ 7…

A:

Q: Evaluate the integral. (Use C for the constant of integration.) 1- 36x2 dx

A:

Q: Evaluate the integral. (Use C for the constant of integration.) 1- sin(x) dx

A:

Q: Find the indefinite integral by using the substitution x = 8 tan(0). (Use C for the constant of…

A:

Q: Evaluate the integral ( Use C for the constant integration) ∫ 11 tan4(x) sec6(x) dx

A: I=∫11tan4x×sec6x dx=11∫tan4x×sec4x×sec2x dx=11∫tan4x×1+tan2x2×sec2x dx                      ⋯⋯(1)

Q: Evaluate the integral. (Use C for the constant of integration.) 2 tan3(x) sec(x) dx

A: Let sec(x)=t sec(x)tan(x)dx=dt tan2(x)=sec2(x)-1 Substituting we get 2 int (t2-1)dt =2 (t3-t)+C…

Q: Find the indefinite integral. (Use C for the constant of integration.) | cosh(5x) dx

A:

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) tan-(5x) dx 1 + 25x2

A: To evaluate the given integral:

Q: Find the indefinite integral. (Use C for the constant of integration.) sec' 4x tan 4x dx

A: Topic- integration

Q: Find the indefinite integral ∫cosh √x / √x dx

A:

Q: Find the general indefinite integral. (Use C for the constant of integration.) + 8x + 7) dx

A:

Q: Find the indefinite integral. (Use C for the constant of integration.) 3 cosh(Vx) dx

A:

Q: Find the general indefinite integral. (Use C for the constant of integration.) sin 2x 9. dx sin x

A: Explanation of the answer is as follows

Q: Find the indefinite integral. (Use C for the constant of integration.) |V tan(4x) sec?(4x) dx

A:

Q: Evaluate the integral. (Use C for the constant of integration.) ∫ 3 tan2(x) dx

A:

Q: Find the indefinite integral. (Use C for the constant of integration.) 2 cosh(Vx) dx

A:

Q: Evaluate the integral. (Use C for the constant of integration.) 9 sin(2x) dx 1 + cos“(x)

A:

Q: Evaluate the integral 1 dx x4 – x2 Note: Use an upper-case "C" for the constant of integration.

A:

Q: Find the indefinite integral using the substitution x = 2 tan(0). (Use C for the constant of…

A:

Q: Find the indefinite integral. (Use C for the constant of integration.) sin x dx 3 + cos x

A:

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) sin(6x) sin(cos(6x)) dx

A: In this question we have to evaluate the integral.

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.