Decide on what substitution to use, and then evaluate the given integral using a substitution. (Use C for the constant of integration.) -2x - 1 | + x + 1)7 dx

Q: Use the Table of Integrals to evaluate the integral. (Use C for the constant of integration.) e40…

A: We have to find

Q: Evaluate the following integrals. Show the solution. 1. S csc? (7x + 5) dx 2. fx? sec (4x³ + 9) dx…

A:

Q: 3tan a sec? x dx (4+3tan=)* 2

A:

Q: 5. If a and b are positive constants, evaluate the following integrals: ,-bx e-ax -e -dx; (a) (b)…

A: The objective is to evaluate: ; where a and b are positive constants.

Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.) |…

A:

Q: f1+z+² /1+z+z? + 3z*dz

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST…

Q: Evaluate the integral. (Use C for the constant of integration.) A) x cos(2x) dx B)e6θ sin(7θ) dθ

A: here we evaluate the integral      (A)   ∫ x cos (2x)dx     (B)  ∫ e6θ sin (70) dθ

Q: 3x?e³+x? + 2xe *°+x² dx

A: SINCE YOU HAVE ASKED MULTI PAL QUESTIONS IN SINGLE REQUEST , WE WILL BE ANSWERING ONLY THE FIRST…

Q: Evaluate this integral. x? (a? – x²)3/2 dx

A:

Q: Decide on what substitution to use, and then evaluate the given integral using a substitution. (Use…

A: ∫xe6x2-4dx

Q: Evaluate the integral: ∫6/[(x+a)(x+b)]dx for the cases where a=ba=b and where a≠b.a≠b. Note: For…

A: The integral, ∫6x+ax+bdx.

Q: 2. Find a) ³ dx b) xdx. Hence, find whether the following integrals exist and, if they do, find…

A: To evaluate the given improper integrals

Q: x2 + 2 dx x° + x •T/2 5. 3 6. t cos (t) dt

A:

Q: Suggest a trigonometric substitution for each integral, and then write the new integral that results…

A:

Q: Evaluate the integrals using the indicated substitutions.

A: “Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.) -6x…

A: To evaluate the integral by making the given substitution. ∫e-6x dx, u = -6x

Q: (D) What is the value of the original integral in terms of x? -30V z2 + 25 X + C 25z

A: Using substitution we have

Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.) 1 9…

A:

Q: Decide on what substitution to use, and then evaluate the given integral using a substitution. (Use…

A: Integrate the above function

Q: Decide on what substitution to use, and then evaluate the given integral using a substitution. 2x V…

A:

Q: T 15 dx The integral is equal to

A:

Q: Using the trigonometric substitution, the integral dx (x² 81) V x2 – 81 is equal to the integral, in…

A:

Q: Evaluate the integral ? e1/x dx x2

A: we have to integrate by using substitute method

Q: Evaluate the given definite integral using appropriate substitution: 8e2a dx @ 4e4 – 4 A © 4e4 + 4…

A:

Q: For what values of a is each integral improper? Explain.

A: (a) consider the integral ∫a5dxx+2.

Q: Find the integrals below. a) J(2x + 3)* dx b) (x?(x³ + 3)6 dx

A: Integrate. ∫2x+34dx=2x+355×1ddx2x+3+C=2x+355×12+C=2x+3510+C

Q: Evaluate the integral. C x² e* dx NOTE: Enter the exact answer.

A: As per guidelines we have to solve one question Please repost the other questions again

Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.) x3…

A:

Q: Find or evaluate the integral by completing the square. (Use C for the constant of integration.) dx…

A:

Q: Decide on what substitution to use, and then evaluate the given integral using a substitution. (Use…

A: Use substitutions to integration

Q: Use the substitution technique to determine the following integrals:

A:

Q: Decide on what substitution to use, and then evaluate the given integral using a substitution. (Use…

A:

Q: Decide on what substitution to use, and then evaluate the given integral using integration.) x² dx…

A:

Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.)…

A:

Q: Decide on what substitution to use, and then evaluate the given integral using a substitution. (Use…

A:

Q: Decide on what substitution to use, and then evaluate the given integral using a substitution. (Use…

A:

Q: Decide on what substitution to use, and then evaluate the given integral using a substitution. (Use…

A:

Q: . Evaluate the integral, if it exists. L(** – 3x/3 + 1) dx а. i (20* -) dx b. 2e* X.

A:

Q: Evaluate the integral.

A: ∫x24-x232dx Put, x=2sinθ⇒1=2cosθ·dθdx⇒dx=2cosθ·dθ

Q: A. Evaluate the following integrals by substitution. 1. Sx(2x? + 3)®dx

A: Put (2x2+3)= t  Differentiating both sides  4x dx= dt

Q: x? dx (x² – 25)5/2

A:

Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.) |…

A:

Q: Evaluate the integral. (Use C for the constant of integration.) e cos(50) de

A:

Q: Find as many integrals as you can using the formulas and techniques you have studied.…

A: (a) part Consider the given integral ∫dxxx2-1 Use the substitution method to find the integral…

Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.)…

A: u=7+x4  .........equation (i)differentiate wrt x on both side dudx=4x3du=4x3dxdu4=x3dx…

Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.) + 9…

A:

Q: The value of the integral is: b 12 f(x) dx = a

A: Given that the graph of the function  To find the definite integral that represents the shaded area

Q: Decide on what substitution to use, and then evaluate the given integral using a substitution. (Use…

A:

Q: d.x -x2-4x

A:

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.