Question

assignment 10: problem 12 (1 point) compute the indefinite integral. \\( \int \frac{1 - \sin^2 x}{\cos x} dx \\) answer: \\( \square + c \\)

Explanation:

Step1: Simplify the numerator

We know the Pythagorean identity \(1 - \sin^{2}x=\cos^{2}x\). So the integrand becomes \(\frac{\cos^{2}x}{\cos x}\).

Step2: Simplify the fraction

Simplify \(\frac{\cos^{2}x}{\cos x}\) (assuming \(\cos x
eq0\)) to get \(\cos x\).

Step3: Integrate the simplified function

The integral of \(\cos x\) with respect to \(x\) is \(\sin x\) (since the derivative of \(\sin x\) is \(\cos x\)). Then we add the constant of integration \(C\).

Answer:

\(\sin x + C\)