Circle all of the following integrals that are improper. No justification is needed. 7 1 dx x – 2 In(x – 3) dæ -1 •3 Vx + 2 dx 2 – r2 3 dx 3x x2 Does dx converge or diverge? Explain your answer.

Q: Evaluate the integral. x? + x + 1 dx (x² + 1)²

A: To evaluate the given integral

Q: 03: Evaluate the following integrals dx (1) S 2x (1+Vx)

A:

Q: 1/6 16 14. Evaluate the integral dx. o V1-9x² 16 8. 8. b. 16 4. d. пе. a. 25л л с. 9Tt 25 9Tt 3 12

A:

Q: V4 +x? xp

A:

Q: 5x х? — х — 6

A: Integration by using partial fraction

Q: valuate the following Integrals 1 -3 +1 dx 4secx tan x- 2 sec? x)dx .3 dx x² +1

A:

Q: II. Evaluate the following integrals: 1. fe²dx 2. 11 tedx J 1+ 3. fx'e* dx e√x+1 √y +1 4. S dy

A: We have to evaluate the given integrals.

Q: 1. Evaluate the following integrals, Debe Justify all steps. x + 4 dx x3 + 3x2 – 10

A: Given:-             fx = x+4x3+3x2-10To determine                     ∫ fx dx

Q: Evaluate the following integral. S- dx 2 x + 6x + 13 arctan dx x² x + 6x + 13 (Type an exact…

A:

Q: a) Jo (3x + 1)5 dx dx b) J3 3 -8

A:

Q: x dx Evaluate the improper integral by using a suitable substitution. x4 + 49

A: To evaluate the improper integral by the suitable substitution.

Q: Evaluate the following integrals using FTOC. 6. (Зх + 7) dx 10. (2+ 2x) dx

A: We need to evaluate the integrals using fundamental theorem of calculus.

Q: (a) fx sin(2x) dx

A: According to bartleby policy we cannot answer multiple questions, we can only answer one question at…

Q: Evaluate the integral. [HINT: Use a shortcut.] 2 2-x + 1 dx

A: The integral is  ∫022-x+1dx

Q: Evaluate one the integrals: 2x-1 8 a) ! -dx 2 X x² + 3x + 1

A: Introduction: Integration is the calculation of an integral. Integrals in mathematics are used to…

Q: Given f(x)=3x^2 + 4x + 5, determine the roots of the function. Verify them with a graph.

A: An algebraic expression is obtained by combining numbers and variables together with arithmetic…

Q: 7. Se* (1 + 2e*)* dx

A:

Q: Evaluate the integral [x³√x² - 60 2 6 dx.

A: .

Q: Which one is an improper integral? O 6 sin(x-5) x-5 S₁º O none O 6 sin(x-5) x-3 O S 6 sin(x-5) x-7…

A: Improper integral:- An improper integral is a definite integral that has either or both limits…

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.