Recent questions tagged goclasses-da-dpp-day-184

Evaluate $$I=\int_0^1 \frac{x^2}{(1-x^2)^{3/2}}dx$$$\frac{\pi}{4}$ $1$ $2$ The integral diverges

Let $f(x)=\left|x-\lfloor x\rfloor-\frac{1}{2}\right|$, where $\lfloor x\rfloor$ denotes the greatest integer less than or equal to $x$. The value of $\int_{0.2}^{2.75} f...

A $20\text{ ft}$ ladder leans against a vertical wall. The base of the ladder is sliding away from the wall at $2\text{ ft/s}$. A point $P$ on the ladder is $6\text{ ft}$...

Let $f:[0,1]\to\mathbb{R}$ be continuous and satisfy $f(x)=x^2+\int_0^1 (x+t)f(t)dt$ for every $x\in[0,1]$. Which of the following is $f(x)$?$x^2-5x-\frac{17}{6}$ $x^2+5x...

Which of the following is the derivative of $f(x)=(x^2+1)^{x\ln x}$ when $x>0$?$(x^2+1)^{x\ln x}\left((\ln x+1)\ln(x^2+1)+\dfrac{2x^2\ln x}{x^2+1}\right)$ $(x^2+1)^{x\ln ...