Question
\(\int x \cos (2x)dx=\)
A \(\frac{1}{2}x^{2}\sin (2x)+C\)
B \(\frac{1}{2}x^{2}\cos (2x)+\frac{1}{2}\sin (2x)+C\)
C \(\frac{1}{2}x\sin (2x)-\frac{1}{4}\cos (2x)+C\)
D \(\frac{1}{2}x\sin (2x)+\frac{1}{4}\cos (2x)+C\)
Answer/Explanation
Question
\(\int_{0}^{1}x\left ( x^{2}+2 \right )^{2}dx=\)
(A) \(\frac{19}{2}\) (B) \(\frac{19}{3}\) (C)\(\frac{9}{2}\) (D)\( \frac{19}{6}\) (E) \(\frac{1}{6}\)
Answer/Explanation
Ans:D
Question
\(\int xe^{2x}dx=\)
(A)\(\frac{xe^{2x}}{2}-\frac{e^{2x}}{4}+C\) (B)\(\frac{xe^{2x}}{2}-\frac{e^{2x}}{2}+C\) (C)\(\frac{xe^{2x}}{2}+\frac{e^{2x}}{4}+C\) (D)\(\frac{xe^{2x}}{2}+\frac{e^{2x}}{2}+C\) (E)\(\frac{x^{2}e^{2x}}{4}+C\)
Answer/Explanation
Question
\(\int_{0}^{1}\sqrt{x}(x+1)dx=\)
(A) 0 (B) 1 (C) \(\frac{16}{15}\) (D) \(\frac{7}{5}\) (E) 2
Answer/Explanation
Ans:C