Question
\(\int_{0}^{8}\frac{dx}{\sqrt{1+x}}\)=
(A) 1 (B) \(\frac{3}{2}\) (C) 2 (D) 4 (E) 6
▶️Answer/Explanation
Ans:D
Question
\(\int_{0}^{1/2}\frac{2x}{\sqrt{1-x^{2}}}dx\)=
(A)\(1-\frac{\sqrt{3}}{2}\) (B)\(\frac{1}{2}In \frac{3}{4}\) (C)\( \frac{\pi }{6}\) 1(D) \( \frac{\pi }{6} -6\) (E)\(2-\sqrt{3}\)
▶️Answer/Explanation
Ans:E
Question
\(\int \frac{5}{1+x^{2}}dx\)=
(A)\(\frac{-10x}{(1+x^{2})^{2}}+C\) (B) \(\frac{5}{2x}In (1+x^{2})+C\) (C)\(5x-\frac{5}{x}+C\) (D)\(5arctanx+C\) (E)\(5In(1+x^{2})+C\)
▶️Answer/Explanation
Ans:C
Question
\(\int_{0}^{1}xe^{-x}dx\)=
(A) 1 −2 e (B) -1 (C) \(1-2e^{-1}\) (D) 1 (E) 2e −1
▶️Answer/Explanation
Ans:C
Question
\(\int \frac{3x^{2}}{x^{3}+1}dx\)=
(A)\(2\sqrt{x^{3}+1+C}\)
(B)\(\frac{3}{2}\sqrt{x^{3}+1+C}\)
(C)\(\sqrt{x^{3}+1+C}\)
(D)\(ln\sqrt{x^{3}+1+C}\)
(E)\(ln(x^{3})+C\)
▶️Answer/Explanation
Ans:A