Practice problem
Rewrite the following as a definite integral:
limn→∞∑i=0∞11+(in)2Δx\lim_{n\to\infty} \sum_{i=0}^{\infty} \frac{1}{1+(\frac{i}{n})^2} \Delta xlimn→∞∑i=0∞1+(ni)21Δx where Δx=(1n)\Delta x = (\frac{1}{n})Δx=(n1)
∫0111+(xn)2 dx\int_{0}^{1} \frac{1}{1+(\frac{x}{n})^2} \,dx∫011+(nx)21dx
∫0111+x2 dx\int_{0}^{1} \frac{1}{1+x^2} \,dx∫011+x21dx
∫01arctanx dx\int_{0}^{1} \arctan{x} \,dx∫01arctanxdx
∫01arctanxn dx\int_{0}^{1} \arctan{\frac{x}{n}} \,dx∫01arctannxdx
Type a concept, like “slope” or “photosynthesis”.