Definitely
int_{1}^{e}\frac{x^2+1}{x}dx
\frac{e^2+1}{2}
intsin^-1(x)dx
xarcsinx+sqrt(1-x^2)+C
\lim_(x\rightarrow0)\frac{sinx-x}{x^3}
-1/6
What is the average rate of change of f(x)=secx on the interval [0, pi/3] ?
(3)/(pi)
For differentiable function f, int_{-3}^{4}f(x)dx=100 and the average value of f(x) on [-5, -3] is 6. Determine int_{4}^{-5}f(x)dx
-112
\int\frac{5x+14}{x^2+8x-20}dx
2ln|x-2|+3ln|x+10|+C
\lim_(x\rightarrow\infty)(1-3/x)^(x)=
1/e^3
What is the average value of f(x)=tanx on the interval [0, pi/3] ?
(3ln2)/pi
\int_{0}^{2}\frac{3x^3+7x^2-x+7}{x^2+1}dx
20-2ln5
int\frac{4x+3}{x^2+10x+26}dx
2ln|x^2+10x+26|-17arctan(x+5)+C
\int_{1}^{\infty}e^-xdx=
1/e
The velocity of a flying flamingo (rectilinear motion) is given by v(t)=t^2-6t+8 m/s . Determine the total distance the flamingo traveled from t=1 to t=5.
4 m
int_{sqrt2}^{sqrt5}30x^3sqrt(x^2-1) dx=
256
inte^xcosxdx
\frac{e^xsinx+e^xcosx}{2}+C
Use the integral test to show that \sum_{n=1}^{\infty}5/n^3 is convergent.
Since \lim_{a\rightarrow\infty}\int_{1}^{\a}5/x^3dx=\frac{5}{2} , the series is convergent by the integral test.
Given g(x)=\int_{0}^{sinx}arcsin(t)dt , determine g'((5pi)/6) .
-(pisqrt3)/12