Recent content by JamesGregory

I was taking the integral of the secant function. Twice... The first one is simple, but what is the integral of ln(secx + tanx)dx? I've tried a few things, the first being integration by parts with u = ln(secx + tanx+) and dv = dx This just cancels in the end to 0 = 0 I also rewrote it as...

This is high school ap calculus ab, and I don't think we've gotten to induction, but I do think I see what you're getting at. but shouldn't u and dv be parts of the original integrand or am I missing something obvious?

Homework Statement Prove the following trigonometric reduction using integration by parts: \int \sin^n x dx = - \frac{\ \sin^{n-1} x \cos x}{n} + \frac{\ n-1}{n} \int \sin^{n-2} x dx 2. The attempt at a solution I tried using integration by parts by breaking up sin^n x into sin^(n-2) x...

Without using explicit geometric or specific terms, you could explain the concept of the integral as a family of functions whose slopes are described by the original function. This is obviously more closely related to the anti-derivative definition of the integral, but it may help you...