Can you suggest some challenging calculus questions? I am a calculus 2 student, just passing high school. I would really appreciate it if you can suggest some cool challenging questions for a high school student with solutions or hints too!
Here are two that I've seen on this network.
Problem 1. Show that
$$
\sum_{n=1}^{\infty}\big(\frac{1}{4n+1}-\frac{1}{4n}\big)=\frac{1}{8}(\pi-8+6\ln 2)
$$
Problem 2. Evaluate the indefinite integral
$$
\int e^{\sin x}(x\cos x-\sec x\tan x)dx
$$
Here are two that I've seen on this network.
Problem 1. Show that
$$
\sum_{n=1}^{\infty}\big(\frac{1}{4n+1}-\frac{1}{4n}\big)=\frac{1}{8}(\pi-8+6\ln 2)
$$
Problem 2. Evaluate the indefinite integral
$$
\int e^{\sin x}(x\cos x-\sec x\tan x)dx
$$