5.3: The Fundamental Theorem of Calculus

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Apr 19, 2024
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- 5.2: The Definite Integral
- 5.4: Substitution

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Use the first part of the fundamental theorem of calculus to find $\displaystyle \frac{d}{dx} \int_1^x e^{-t^2}\ dt$ .
Use the first part of the fundamental theorem of calculus to find $\displaystyle \frac{d}{dx} \int_3^x \sqrt{9 - t^2}\ dt$ .
Use the first part of the fundamental theorem of calculus to find $\displaystyle \frac{d}{dx} \int_{-5}^x \dfrac{\cos s}{1 + s^2}\ ds$ .
Use the first part of the fundamental theorem of calculus to find $\displaystyle \frac{d}{dx} \int_0^{2x} \tan(t^2)\ dt$ .
Use the first part of the fundamental theorem of calculus to find $\displaystyle \frac{d}{dx} \int_0^{\sin x} \frac{1}{\sqrt{1 - y^2}}\ dy$ .
Use the first part of the fundamental theorem of calculus to find $\displaystyle \frac{d}{dx} \int_x^3 \ln(t)\ dt$ .
Use the first part of the fundamental theorem of calculus to find $\displaystyle \frac{d}{dx} \int_{1 - x}^{x^2} (2t^2 - 3t)\ dt$ .
Use the second part of the fundamental theorem of calculus to calculate $\displaystyle \int_{-1}^2 3x^2\ dx$ .
Use the second part of the fundamental theorem of calculus to calculate $\displaystyle \int_{-2}^3 (x^2 + 3x - 5)\ dx$ .
Use the second part of the fundamental theorem of calculus to calculate $\displaystyle \int_{-2}^3 (t+2)(t-3)\ dt$ .
Use the second part of the fundamental theorem of calculus to calculate $\displaystyle \int_{1}^4 \left(\sqrt{x} + \dfrac{1}{\sqrt{x}}\right)\ dx$ .
Use the second part of the fundamental theorem of calculus to calculate $\displaystyle \int_{1}^2 \dfrac{2z^4 + z^3 - 3z}{z^3}\ dz$ .
Use the second part of the fundamental theorem of calculus to calculate $\displaystyle \int_{0}^{2\pi} \cos \theta\ d\theta$ .
Use the second part of the fundamental theorem of calculus to calculate $\displaystyle \int_{0}^{\pi/2} \sin \theta\ d\theta$ .
Use the second part of the fundamental theorem of calculus to calculate $\displaystyle \int_{0}^{\pi/4} \sec^2 \theta\ d\theta$ .
Use the second part of the fundamental theorem of calculus to calculate $\displaystyle \int_{\pi/6}^{\pi/4} \sec \theta \tan \theta\ d\theta$ .

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