MCQ
$\int_{}^{} {{a^x}\;da = } $
- A$\frac{{{a^x}}}{{{{\log }_e}a}} + c$
- B${a^x}{\log _e}a + c$
- ✓$\frac{{{a^{x + 1}}}}{{x + 1}} + c$
- D$x{a^{x - 1}} + c$
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
$f(x)=\left|\begin{array}{ccc} \sin ^{2} x & 1+\cos ^{2} x & \cos 2 x \\ 1+\sin ^{2} x & \cos ^{2} x & \cos 2 x \\ \sin ^{2} x & \cos ^{2} x & \sin 2 x \end{array}\right|, x \in R \text { is }$
$I.$ $P\,({A^c}/{B^c}) = \frac{3}{4}$
$II.$ The events $A$ and $B$ are mutually exclusive
$III.$ $P(A/B) + P(A/{B^c}) = 1$
(There are two questions based on $PARAGRAPH "II"$, the question given below is one of them)
($1$) The value of $2 \int^{\frac{\pi}{2}} f(x) g(x) d x-\int^{\frac{\pi}{2}} g(x) d x$ us
($2$) The value of $\frac{16}{\pi^3} \int_0^{\frac{\pi}{2}} f(x) g(x) d x$ is
Give the answer or quetion ($1$) and ($2$)