4.8: Antiderivatives
- Page ID
- 144290
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- Evaluate \(\displaystyle \int 3\ dx\).
- Evaluate \(\displaystyle \int 2x^3\ dx\).
- Evaluate \(\displaystyle \int (4x + \sqrt{x})\ dx\).
- Evaluate \(\displaystyle \int \cos x\ dx\).
- Evaluate \(\displaystyle \int \left(\dfrac{2}{x^2} - \dfrac{x^2}{2}\right)\ dx\).
- Evaluate \(\displaystyle \int \dfrac{3x^2 + 2}{x^2}\ dx\).
- Evaluate \(\displaystyle \int \left(\sec x \tan x + \dfrac{4}{x}\right)\ dx\).
- Evaluate \(\displaystyle \int (4\sin x - 3\sec^2 x)\ dx\).
- Evaluate \(\displaystyle \int \dfrac{5x^4 + 3x^2 + 7}{x^3}\ dx\).
- Evaluate \(\displaystyle \int (2e^x - 5x^{-5/2})\ dx\).
- Find the function \(f\) with \(f'(x) = x^{-2}\) and \(f(2) = 3\).
- Find the function \(g\) with \(g'(x) = \sqrt{x} + x^2\) and \(g(0) = 2\).
- Find the function \(h\) with \(h'(x) = \dfrac{1}{\pi} - 3\sec x\tan x\) and \(h(\pi) = 7\).
- Find two possible functions \(f\) such that \(f''(x) = x^2 + 2\).
- Find two possible functions \(g\) such that \(g''(x) = e^x + \dfrac{1}{2x^2}\).
- Find two possible functions \(h\) such that \(h'''(x) = \sin x\).