Evaluate the integral ∫−10(x−9)(x+5)(x−2)dx∫−10(x−9)(x+5)(x−2)dx   Note: Use an upper-case "C" for the constant of integration.

Q: Evaluate the integral. (Use C for the constant of integration.) 33 + 8x – x² dx

A: Given integral, ∫33+8x-x2 dx

Q: Evaluate the integral. (Use C for the constant of integration.) (x2.8 + x-1.2) dx

A: Power rule

Q: (2x- 1) dx x2 - 15x + 56

A:

Q: Evaluate the integral. (Use C for the constant of integration.) 3 dx x(x4 + 5)

A: In this integrated we will assume x4 =t , then we will solve it

Q: Find the indefinite integral. (Use C for the constant of integration.) -0.2x е dx

A: We have to find indefinite integration: ∫e-0.2xdx In this case we use substitution method, so let…

Q: Use the basic integration rules to find or evaluate the integral.

A: Indefinite integral, also known as antiderivative, is a function F(x)=∫f(x)dx such that F'(x)=f(x).…

Q: Evaluate the integral. (Use C for the constant of integration.) √x²√3 dx √3+2x-x²

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: Find the general indefinite integral. (Use C for the constant of integration.) (7x2 + 5x-2) dx

A:

Q: Evaluate the integral. (Use C for the constant of integration.) x2 + 7x + 1 dx (x2 + 1)2

A:

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) xV7 - x2 dx

A:

Q: Evaluate the integral. (Use C for the constant of integration.) +² | dx 81-x²

A:

Q: Find the general indefinite integral. (Use C for the constant of integration.) 4x - 9/x dx

A: To find the indefinite integral: ∫4x3-9xxdx Solution: Evaluating the given integral.…

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

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

Q: Evaluate the integral. (Use C for the constant of integration.) x² - 64 dx - +8

A:

Q: Evaluate the integral. (Use C for the constant of integration.) 9x dx

A:

Q: Evaluate the integral. (Use C for the constant of integration.) x2 dx 25 – x2

A: Let, Integrate using substitution,

Q: Evaluate the integral 8 dx x² V25 – x2 Note: Use an upper-case "C" for the constant of integration.

A:

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 general indefinite integral. (Use C for the constant of integration.) + 9x3.5) dx

A:

Q: Find the general indefinite integral. (Use C for the constant of integration.) 7x2 ) dx

A:

Q: Evaluate the integral –4x3/2 In(x) dx, x >0 Note: Use an upper-case "C" for the constant of…

A: Evaluate the integral

Q: Evaluate the integral. (Use C for the constant of integration.) х dx x2 + x + 3

A:

Q: Find the general indefinite integral. (Use C for the constant of integration.) (5x2 + 6x-2) dx

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.) 6x 6 dx

A: We have to solve integration by using exponential integral formula.

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) dx (6x – 5)2

A:

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

A:

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

A:

Q: Evaluate the integral. (Use C for the constant of integration.) 17xe2x dx (1 + 2x)?

A:

Q: Evaluate the integral. (Use C for the constant of integration.) x + 21 dx x2 + 24x + 148

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

Q: Evaluate the integral. (Use C for the constant of integration.) 45x-5 dx

A: Consider the given integral. ∫45x-5dx The objective of the problem is to evaluate the given…

Q: please answer the question and show all of your work

A:

Q: Evaluate the integral. (Use C for the constant of integration.) x2 - 64 dx

A: The given integral is ∫x2-64x3dx. Let us assume u=x2-64 and v'=1x3. Differentiate u with respect to…

Q: Evaluate the integral. (Use C for the constant of integration.) 7-6x - x² dx

A:

Q: Evaluate the integral. (Use C for the constant of integration.) 11 dx x²V 4x² - 1

A: Given integral ∫11dxx24x2-1=11∫dxx24x2-1 Now consider ∫dxx24x2-1 Use substitution method to solve…

Q: Evaluate the integral. (Use C for the constant of integration.) (2× – 5*) dx

A:

Q: Evaluate the integral. (Use C for the constant of integration.) x² - 36 dx v3

A:

Q: Evaluate the integral. (Use C for the constant of integration.) (3* – 5*) dx

A:

Q: Find the general indefinite integral. (Use C for the constant of integration.) 8x + 4 + dx x2 + 1

A:

Q: Evaluate the integral. (Use C for the constant of integration.) dx 5x(1 +5x)

A: Evaluate the integral using trigonometric substitution

Q: Evaluate the integral. (Use C for the constant of integration.) (7 – 17x) dx

A: We can solve the indefinite integration.

Q: Evaluate the integral. (Use C for the constant of integration.) (3× – 5*) dx

A:

Q: Evaluate the integral. (Use C for the constant of integration.) 4e2x dx 5 + ex

A:

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

A:

Q: Evaluate the integral. (Use C for the constant of integration.) 13 dx xV 9x2 - 1

A:

Q: Evaluate the integral. (Use C for the constant of integration.) 27 – 6x – x2 dx

A:

Q: Evaluate the integral. (Use C for the constant of integration.) 6x2 + 8x + 3) dx

A: ∫16x3-6x2+8x+3 dx

Q: Evaluate the integral. (Use C for the constant of integration.) | (x – 3)sin(xx) dx

A: The given integral:∫x-3sinπxdxWe need to evaluate the above integral.We will use integral by parts…

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.