In at least 10 sentences, what can you learn about the Fundamental Theorem of Calculus and Definite Integral?

Q: Use the Fundamental Theorem of Calculus, Part I, to evaluate d de -dt

A: We have to find

Q: State and prove the first fundamental the orem of calculus and its importance?

A:

Q: What nature of Fundamental Theorem of Calculus helps us to evaluate the definite integrals?

A: Given: To explain briefly about What nature of Fundamental Theorem of Calculus helps us to evaluate…

Q: Evaluate the definite integral: dr 1+ 16z2

A: Find the given integral

Q: Please provide 50 formulas in Diffential and Integral Calculus.

A: Topic:- formulas in Diffential and Integral Calculus.

Q: The integral from 2 to infinity of 6/((x+5)^(3/2))

A: ∫2∞6x+532

Q: Use the Fundamental Theorem of Calculus to evaluate the following definite integral:

A:

Q: Evaluate the integral. sec (5x + 8) tan (5x + 8) dx

A: ∫ sec5x+8tan5x+8dx

Q: 2 178. 1x

A:

Q: Evaluate the integral by interpreting it in terms of areas.

A: The given integral ∫0732x-9dx

Q: Proves/1=L2

A: The given figure is

Q: Use a linear approximation to estimate the value of the fifth root of thirty (Answers are to be…

A: To determine: 305 using the linear approximation   Formula used: Linear approximation of f(x) at x =…

Q: Use the Fundamental Theorem of Calculus to cvaluate (1 - da

A: Integrate using fundamental theorem of calculus.

Q: Evaluate the definite integral by interpreting it in terms of areas. 8 | (2x – 14)dr 12

A:

Q: „T/2 sinOdo 183.

A:

Q: (6x5+2x) dx

A:

Q: Evaluate the definite integral by interpreting it in terms of areas. 7 (3x - 12)da 3

A:

Q: 3x+2 + dt 1++5

A: Given  Fx=∫13x+2t1+t5dt

Q: In at least 4 sentences, write what you have learned in Fundamental Theorem of Calculus and Definite…

A:

Q: In your own words, describe Rolle’s Theorem.

A: To describe: Roll's theorem

Q: dr 5. 2 ?+3 2

A:

Q: the integral of tan^5 (x) sec^3 (x)dx

A: we will find integral  of f(x) using rule as mentioned above

Q: Evaluate the integral. eu + 3 du -3

A: ∫-31eu+3 du

Q: Evaluate each definite integral using the Fundamental Theorem of Calculus, Part 2. 181.  16 ∫…

A: By Fundamental theorem of calculus .part 2  ∫abf(x)dx=F(b)-F(a) where f(x) is continuous on the…

Q: Solve the integral 10. (tan 2x + sec 2x)³dx

A: Given integral is: I=∫tan 2x+sec 2x3dx We have to find the value of this integral.

Q: State the first part of the Fundamental Theorem of Calculus (FTC).

A: The first part of fundamental theorem of calculus states that -

Q: x4/3' dx -1 | --

A:

Q: 2x* dx

A: Here is the solution

Q: 9. Demonstrate the method of the Fundamental Theorem of Calculus to find the following definite…

A: our objective is to find the definite integral.

Q: 3 26x° + 600 dxr

A:

Q: Find the derivative of 4 ^ (3x) * O 12x O In 4 O x In 64 O (4^(3x)) In 64

A: We can solve this question taking derivative of both side wrt x

Q: Use a linear approximation to estimate the value of the fifth root of thirty (Answers are to be…

A:

Q: How was the birth calculus attained?

A: Calculus was borned, rather developed independently by Newton and Leibniz, this marked as one of the…

Q: The integral of tan^2 (x) sec^4 (x) dx

A: To determine the given trigonometric  integral.

Q: Use the Fundamental Theorem of Calculus Part II to compute 0. 4 sec (x) dr.

A: Proceed as shown below

Q: sec 3B tan 3BdВ

A:

Q: Find all integral solutions of 188 x + 140 y = 4

A: Given equation: 188x +140y = 4

Q: du

A:

Q: Explain in your own words what the Fundamental Theorem of Calculus says. Be sure to address both…

A:

Q: 13 1 (1+2x)?

A: We have to integrate the given integral

Q: In x 5. Evaluate the indefinite integral.

A: Substitute, ln x = t  = x = et differentiate both sides 1/x dx = dt ∫ ln x/x5 dx = ∫ t/x4(dx/x) = ∫…

Q: Use the definite integral and the Fundamental Theorem of Calculus to solve the following problem.

A:

Q: Discuss the two versions of the fundamental theorem of calculus

A: This the problem of Real Analysis, Theory of Reimann Integration.

Q: | У49х2 + 1225 dx

A: We have to find

Q: lime

A: The epsilon-delta definition of limits:   The limit of f(x) at x = c is L if for any ε>0 there's…

Q: 8. Ssin(1 – Int)dt

A:

Q: Vx3 (х + 5)dx.

A: