Differentiating an Integral Function (Half of FTC)
Read this topicExplanations 4
- As mentioned previously, the first Fundamental Theorem of Calculus relates the derivative of a function to its antiderivative. Let's begin with an example: Of course, we can cal…
By Steven Kwon, Victor Wang, Alexander Mason, Alex Federspiel, Moor Xu
- Consider an arbitrary function, and denote aaa and bbb as two different values such that the function, fff, is continuous on [a,b][a,b][a,b]. Finally, suppose that ttt is some v…
By Brandon Lin, Moor Xu
- Happy Thanksgiving, reader! How about try out these problems? Lol, have fun!
By Freya Edholm
- (Video) Fundamental Theorem of Calculus - Part 1 by PatrickJMT Here's a video by patrickJMT where he explains the Fundamental Theorem of Calculus Part 1 and how you can solve pr…
By Alex Federspiel, Gabi Slizewska
Problems 10
- Let f(x)=∫2xet2dtf(x) = \int_2^x e^{t^2} dtf(x)=∫2xet2dt for all reals xxx. What is the value of ln(f′(10))\ln(f'(10))ln(f′(10))?
- Let f(x)=∫23et2dtf(x) = \int_2^3 e^{t^2} dtf(x)=∫23et2dt for all reals xxx. What is the value of ln(1+f′(10))\ln(1+f'(10))ln(1+f′(10))?
- Suppose we have a function f(x)f(x)f(x) that is differentiable, such that f′(x)f'(x)f′(x) is continuous. Evaluate whether the following two statements are true or false. (1) f(x…
- Find the derivative of the function given that, g(x)=∫0xt2+t−13tdtg(x)=\int_0^x \frac{t^2+t-1}{3^t}dtg(x)=∫0x3tt2+t−1dt
- Find the derivative of the function given that, g(x)=∫0xt14dtg(x)=\int_0^x t^{14}dtg(x)=∫0xt14dt
- Find the derivative of the function given that, g(x)=∫x6sin(t2)dtg(x)=\int_x^6 \sin(t^2)dtg(x)=∫x6sin(t2)dt
- Find the derivative of the function given that, g(x)=∫x3e4dtg(x)=\int_x^3e^4dtg(x)=∫x3e4dt
- Find the derivative of the function given that g(t)=∫4x2t2+2t dtg(t)=\int_4^{x^2}t^2+2t\text{ }dtg(t)=∫4x2t2+2t dt
- Find the derivative of the function given that g(t)=∫xxetdtg(t)=\int_{\sqrt x}^{x}e^tdtg(t)=∫xxetdt
- Find the derivative of the function given that g(t)=∫x2sinxlnt dtg(t)=\int_{x^2}^{\sin x}\ln t \text{ }dtg(t)=∫x2sinxlnt dt