Calculate the following antiderivative. Show your work. \int \left( x+ \frac {1}{x}-\sin (x) \right ) dxFind the following antiderivatives: a) \int x^6 dx b) \int x^\frac{-1}{2} dx c) \int (2x^5 - \frac{3}{x^5}) dx...
Calculate the antiderivatives of the following {eq}\frac{d}{dx} ( \cos ( 5 \sin(t/3)) \\ \frac{d}{dx} (x^2(x^3-1)^5) \\ \frac{d}{dx} (\frac{1+\sin 3t}{3-2t})^{-1} {/eq} Integration and Differentiation: Both Integration and Derivative are units of the calculus...
From there, we look at [∂nx,xm][∂xn,xm] and the first option is that its derivative gets taken once: the derivative is mxm−1mxm−1 and there are nn derivative operators that can do it. Then we want two derivatives, then three: so if in commuting the deri...
The leading and trailing zeros are not significant figures. Zeros between non-zero numbers are always significant. Besides this tool you can also use our logarithm and anti-logarithm calculator. How to use Sig Fig Calculator & Counter (With Rounding)? To use sig fig rounder, you need to fol...
Integration techniques can be used to find antiderivatives of a trigonometric function. Sometimes trigonometric identities may be needed to do so. To solve this problem, we'll apply the integral sum rule and Use the common integral: ∫1x2+1dx=arctan(x)...
wise smooth simple closed curve in the plane and let D be the region bounded by C. If P and Q have continuous partial derivatives on an open region which contains D and {eq}\vec{F}=P\vec{i}+Q\vec{j},then\\ \in...
Understand what derivative calculus is and how to find the derivative of a function. Learn the derivative rules, and practice taking derivatives by following examples. Related to this Question Calculate the derivative of the following function. y = \frac{e^{2x{1 + e^{2x ...
Calculate the following antiderivatives: A) Integral of 6t - 3t^6 + 10 dt. B) Integral of 1/(u^(7/4)) + 6.5 sqrt(u) du. C) Integral of 1/(5x^3) dx. Use the Fundamental Theorem of Calculus to evaluate the derivative of the following function. integral 2^e^x + ...
Anti-Derivatives: Calculating Indefinite Integrals of Polynomials from Chapter 13 / Lesson 2 18K The fundamental theorem of calculus allows us to calculate indefinite integrals as the anti-derivatives of the original polynomial function. Learn how to calculate indefinite integrals of polynomials through...
Note that when the upper bound is instead a function ofx, we can use this in combination with the chain rule. In general, this looks like ddx∫au(x)f(t)dt=ddu(∫au(x)f(t)dt)dudx=f(u)dudx Answer and Explanation:1 Note that they have written the variables bac...