Question
\(\int 2^{x}dx=\)
A \(2^{x}\)+ C
B \((\ln 2)2^{x}\)+ C
C \(\frac{x^{2}}{\ln 2}\)+C
D \(\frac{2^{x+1}}{x+1}\)+C
Answer/Explanation
Question
\(\frac{dy}{dx} \)= tanx, then y=
(A)\(\frac{1}{2}tan^{2}x+C \) (B) \(sec^{2}x+C\) (C) In|secx|+C (D)In|cos|+C (E)secx tanx+C
Answer/Explanation
Ans:C
Question
Evaluate the integral \(\int (x^{4}-3x^{2}+1)dx\).
(A) \(\frac{x^{5}}{5}-\frac{3x^{3}}{2}+x+c\)
(B) \(4x^{3}-6x+c\)
(C) \(\frac{x^{4}}{4}-\frac{3x^{2}}{2}+x+c\)
(D)\(\frac{x^{5}}{5}-x^{3}+x+c\)
Answer/Explanation
Ans:(D)
Question
Evaluate \(\int \frac{x^{2}+3x-10}{x-2}dx\)
(A) \(\ln \left | x-2 \right |\left ( \frac{1}{3}x^{3}+\frac{3}{2}x^{2} -10x\right )+c\)
(B)\(\frac{\frac{1}{3}x^{3}+\frac{3}{2}x^{2}-10x}{(x-2)^{2}}+c\)
(C) \(\frac{1}{2}x^{2}+5x+c\)
(D) \(\left ( 2x+3 \right )\ln \left | x-2 \right |+c\)
Answer/Explanation
Ans:(C)