Fundamental Theorem of Calculus

Welcome to the "Fundamental Theorem of Calculus" category on Questions LLC, your go-to destination for all things related to this fundamental concept in mathematics. Whether you're a student seeking clarification or an enthusiast who wants to deepen their understanding, this category is here to provide you with a wealth of questions and answers about the Fundamental Theorem of Calculus. Explore a variety of topics, from its historical background to its practical applications, and delve into the intricacies of this theorem that connects differential calculus with integral calculus. Let us be your guide as we unravel the mysteries of this crucial theorem and empower you to unlock new insights and solve complex problems.

Questions (39)

Using the Fundamental Theorem of Calculus solve:F(x)= ∫ Cos(t^2) + t dt on interval [x to 2] FTC = [∫f(x)]' on interval [0
1. 2 answers
2. asked by Celine
3. 1,278 views
A very important questionThe sum of the derivative and integral of a Function equals what?
1. 2 answers
2. asked by Dave
3. 48 views
(1 point) This is similar to a problem from the Hughes-Hallett textbook. Use the Fundamental Theorem of Calculus to evaluate the
1. 3 answers
2. asked by anonymous
3. 548 views
Evaluate exactly, using the Fundamental Theorem of Calculus:∫^s_06e^xdx=
1. 1 answer
2. asked by Destiny Padgett
3. 65 views
Evaluate exactly, using the Fundamental Theorem of Calculus:∫^r_0(x^4/7+8x)dx=
1. 1 answer
2. asked by Destiny Padgett
3. 76 views
Evaluate exactly, using the Fundamental Theorem of Calculus:∫^s_06e^xdx=
1. 1 answer
2. asked by Destiny Padgett
3. 83 views
d/dx integral from o to x of function cos(2*pi*x) du isfirst i do the integral and i find the derivative right. by the
1. 1 answer
2. asked by david
3. 971 views
for the function F(t)=ln(t^2), let f(t)=F'(t). Write the integral from a to b of f(t) dt and evaluate it with the fundamental
1. 5 answers
2. asked by bob
3. 7,829 views
Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.g(x) = e^(3t^2) − 3t dt from 4 to x
1. 3 answers
2. asked by jessica
3. 1,297 views
For the function F(t)=3^t, let f(t)=F′(t). Write the integral ∫^{b}_a f(t)dt and evaluate it with the Fundamental Theorem of
1. 3 answers
2. asked by Adrian
3. 105 views
The graph of a function f is shown. Let g be the function thatrepresents the area under the graph of f between 0 and x. (a) Use
1. 4 answers
2. asked by Jassan
3. 1,531 views
Use the fundamental theorem of calculus to find the derivative ofg(x)=|e^x top, 0 bottom, cot(t^2) dt
1. 1 answer
2. asked by ChyKia
3. 150 views
Use the Fundamental Theorem of Calculus to find the derivative off(x)=∫[4,x^2]((1/4)t^2−1)^15 dt
1. 3 answers
2. asked by Anon
3. 589 views
Suppose F(t) is an antiderivative of t^{3}. Then F'(t)= t^3.According to the Second Fundamental Theorem of Calculus, x ∫
1. 2 answers
2. asked by James
3. 574 views
Fundamental Theorem of Calculus1. (4e^x-3)dx plus the number in x (6,1)
1. 5 answers
2. asked by Daniel
3. 576 views
Use part 1 of the Fundamental Theorem of Calculus to find the derivative ofg(x)= integrate from 9x to 4x of ((u+4)/(u-1))du
1. 2 answers
2. asked by bobby
3. 527 views
f'(sinx)=cos^2x,f'(1)=1 then f(x)=
1. 3 answers
2. asked by bhavana
3. 376 views
Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.If f(x)= ∫(4,x^3)√(t^2+10) dt then
1. 1 answer
2. asked by dania
3. 644 views
the fundamental theorem of calculus,f(x)=∫(0,x) t^3+2t^2+ 2 dt, and find f"(x). my answer was: f'(x)=x^3+x^2 f"(x)=3x^2+2x it
1. 3 answers
2. asked by MILY
3. 977 views
the fundamental theorem of calculus,f(x)=∫(0,x) t^3+2t^2+2dt, and find f"(x). my answer was: f'(x)=x^3+x^2+2 f"(x)=x^4/4 +
1. 2 answers
2. asked by lindsay
3. 488 views
Section The fundamental Theorem of Calculus:Use Part I of the fundamental Theorem to compute each integral exactly. 4 | 4 / 1 +
1. 1 answer
2. asked by Sandra Gibson
3. 445 views
Use the fundamental theorem of calculus to find the area bounded by f(x)=3 square root of x+2x and the x-axis between x-=0 and
1. 1 answer
2. asked by Ihg
3. 444 views
Use the Fundamental Theorem of Calculus to find the derivative ofg(x)=1/(1+t^5)dt in the interval 1 to x.
1. 1 answer
2. asked by HELP!!!!
3. 452 views
Use 2nd Fundamental Theorem of Calculus to find derivative of f(x) = integral of 2x^2 (at the top) to x-5 (at the bottom) of
1. 2 answers
2. asked by Nick
3. 499 views
I factored and simplified dy/dx of192x^5 + 96x^3 + 12x all the way down to x^2 = u = (-1/2) and (-1/6). How does the result
1. 1 answer
2. asked by John
3. 415 views
d/dx integral from o to x of function cos(2*pi*x) du isfirst i do the integral and i find the derivative right. by the
1. 2 answers
2. asked by david
3. 1,273 views
Let F(x)= the integral from 0 to 2x of tan(t^2) dt. Use your calculator to find F″(1)By applying the fundamental theorem of
1. 3 answers
2. asked by Anonymous
3. 2,238 views
Use the Fundamental Theorem of Calculus to find the area of the region bounded by the x-axis and the graph of y = 4 x3 − 4 x.A
1. 1 answer
2. asked by Erika
3. 889 views
Use the second fundamental theorem of calculus to find F'(x)F(x)=The integral from 0 -> x^2 (Sin(x)^2)dx
1. 2 answers
2. asked by Erika
3. 791 views
I have two questions, because I'm preparing for a math test on monday.1. Use the fundamental theorem of calculus to find the
1. 1 answer
2. asked by Jennifer
3. 779 views
Use the Fundamental Theorem of Calculus to find G'(x) if:/x² G(x)= / cos t dt / 1
1. 2 answers
2. asked by Jay
3. 649 views
Find the derivative of the following function using the appropriate form of the Fundamental Theorem of Calculus.intergral
1. 2 answers
2. asked by Brady
3. 623 views
Use the Fundamental Theorem of Calculus to find G'(x) if:G(x)=∫ up(x²) bottom(1) cost dt
1. 2 answers
2. asked by Jay
3. 600 views
Using the Fundamental theorem of Calculus find the derivative ofF(x) = sec(3x) + ∫ [e^-(t^(2))] Integral from ( 0 to tan(3x) )
1. 2 answers
2. asked by Cold
3. 592 views
Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function h(x)=integral [2,1/x]sin^4t dt
1. 2 answers
2. asked by Eileen
3. 575 views
Use part I of the Fundamental Theorem of Calculus to find the derivative ofg(x)= integrate from 9x to 4x of ((u+4)/(u-1))du
1. 2 answers
2. asked by bobby
3. 537 views
Why do we end up with f(x) instead of f(t) on the second fundamental theorem of calculus?
1. 2 answers
2. asked by Jose
3. 474 views
using the fundamental theorem of calculus what is the derivative of the definite integral from x^3 to sqrt x of (sqrt t) sin t
1. 3 answers
2. asked by adela
3. 478 views
explain why the average change from the start of a period to the end is also zero?
1. 1 answer
2. asked by Anita
3. 457 views