Question

1.Find ff if f′′(x)=2+cos(x),f(0)=−7,f(π/2)=7.f″(x)=2+cos⁡(x),f(0)=−7,f(π/2)=7.

f(x)=

2.Find f if f′(x)=2cos(x)+sec2(x),−π/2<x<π/2,f′(x)=2cos⁡(x)+sec2⁡(x),−π/2<x<π/2, and f(π/3)=2.f(π/3)=2.

f(x)=

3.

Find ff if f′′(t)=2et+3sin(t),f(0)=−8,f(π)=−9.

f(t)=

4.

Find the most general antiderivative of f(x)=6ex+9sec2(x),f(x)=6ex+9sec2⁡(x), where −π2<x<π2.

f(x)=

5.

Find the antiderivative FF of f(x)=4−3(1+x2)−1f(x)=4−3(1+x2)−1 that satisfies F(1)=8.

f(x)=

6.

Find ff if f′(x)=4/sqrt(1−x2)  and f(1/2)=−9.

Answer 1