5. What is piece-wise defined f Evaluate the following integral 1 Lia) dx (b) S (1+x2)

Q: 9. State and prove the Mean Value Theorem for Definite Integrals by applying the Mean Value Theorem…

A: We have to prove the mean value theorem.

Q: 4. Let f(x) = 4x22/3-19x71/11 Determine the largest n for which f E C". %3D

A:

Q: se the midpoint rule with n = 6 to estimate the value of the integral (x³ + x)dx.

A:

Q: y

A: In the given question, concept of area under graph is applied. Area Under Curve Different methods…

Q: (b) 12 sec² 3x 1.² 0 6 + tan 3x dx

A:

Q: Determine the following integrals a) f x^5 dx b) f 8 dx

A: (a) Evaluate the given integral as follows. ∫x5 dx=x5+15+1+C=x66+C Therefore, the value of the given…

Q: Find the value of r*d(\x[³).

A:

Q: d) [ ²³ f(x) dx = = 0 11

A: Consider the given figure,The objective is to evaluate the integral .Formulas use:Area of triangle…

Q: Express lim as a definite integral, f(x)dx. n 0 n i=1

A: Explained below

Q: Evaluate the integral: sec² x dx. tan x

A:

Q: S (1 + In x)² x -dx

A:

Q: Use the Midpoint Rule to evaluate the integral Sx-dx.

A: Midpoint rule:Let f(x) is a polynomial of degree ⩽n-1Let the midpoint x1=a+b2 and…

Q: Evaluate the integral ſ (In x)" X dx

A:

Q: Q1) Evaluate the following integral: y : tanx dx

A: To solve this question, We will use the identity- 1+tan2x = sec2x

Q: 7. Evaluate the definite integrals: a) L, (x2 +1) dx b) 3x dx

A: