Question
\(\begin{Bmatrix}
f(x)=8-x^{2} for -2\leq x\leq 2& & \\
f(x)=x^{2} & &
\end{Bmatrix} \int_{-1}^{3}\) then is a number between
(A) 0 and 8 (B) 8 and 16 (C) 16 and 24 (D) 24 and 32 (E) 32 and 40
Answer/Explanation
Ans:D
Question
\(\int_{0}^{\pi /4}tan^{2}xdx\)=
(A)\(\frac{\pi }{4}\) (B)\(1-\frac{\pi }{4}\) (C)\(\frac{1}{3}\) (D)\(\sqrt{2}-1\) (E)\(\frac{\pi }{4}+1\)
Answer/Explanation
Ans:B
Question
\(\int_{1}^{2}\frac{x-4}{x^{2}}dx\)
(A)\(-\frac{1}{2}\) (B)In2-2 (C)In2 (D)2 (E)In2+2
Answer/Explanation
Ans:B
Question
If \(f(x)=\int_{\frac{\pi }{2}}^{x}\tan ^{-1}tdt\) find \(f{}’\left ( \frac{\pi }{6} \right )\) to the nearest thousandth.
(A) -0.4823
(B) 0.4823
(C) 0.5236
(D) 0.5774
Answer/Explanation
Ans:(B)
Question
If \(f(x)=e^{2x}\) and \(f'(x)=2e^{2x}\) , find \(\int_{2}^{4}f'(x)dx\)
(A) \(\frac{e^{4}(e^{4}-1)}{2}\)
(B) \(e^{4}(e^{4}-1)\)
(C) \(2e^{4}(e^{4}-1)\)
(D) \(4e^{4}(e^{4}-1)\)
Answer/Explanation
Ans:(B)