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Antiderivatives

This is the opposite of the derivative - and it's an integral part of Calculus. It's uses range from basic integrals to differential equations, with applications in Physics, Chemistry, and Economics.

Integration of Trigonometric Functions

         

Find the indefinite integral \(\int{11\tan^6 x \sec^4 x}dx.\)

Find the indefinite integral \(\displaystyle \int{23\tan^5 \theta \sec^7 \theta}d\theta.\)

If \[ f(\theta) = \int \frac{\sin^3 \theta - \cos^3 \theta}{\sin \theta - \cos \theta} d\theta + \int (1- \sin \theta \cos \theta) d\theta\] and \(f(0) = 10,\) what is the value of \(f(30)?\)

Evaluate \[ \int_{-4}^{7}\left( \sin x+4\cos x \right)^2 dx + \int_{-4}^{7}\left( 4\sin x-\cos x \right)^2 dx.\]

What is the value of \(N = \int_0^{\pi} \sin x\ dx\)?

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