If \( f(x)=\int 2^{\sin x \log _{2} e}\left(\frac{5 \cos x+\cos ^{3} x}{(2-\sin x) \sqrt{3+\cos ...
If \( f(x)=\int 2^{\sin x \log _{2} e}\left(\frac{5 \cos x+\cos ^{3} x}{(2-\sin x) \sqrt{3+\cos ^{2} x}}\right) d x \) and \( f(0) \) \( =1 \), then \( f(\pi / 2) \) is equal to
(a) \( \frac{e}{\sqrt{3}} \)
(b) \( (\sqrt{2}) e \)
(c) \( (\sqrt{3}) e \)
(d) \( 2 e \)
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live
Other Videos By PW Solutions
| 2023-06-09 | \( \frac{\int\left(x^{2}+1\right) e^{x}}{(x+1)^{2}} d x=f(x) e^{x}+C \), Where \( C \) is consta... |
| 2023-06-09 | The value of \( \int e^{x^{2}}(2 x-\cot x)\left(x^{2}-\ln (\sin x)\right)(\operatorname{cosec} x... |
| 2023-06-09 | Evaluate: \( \int \sin 4 x \cdot e^{\tan ^{2} x} d x \) |
| 2023-06-09 | If \( I_{n}=\int(\sin x+\cos x)^{n} d x \) and \( I_{n}=\frac{1}{n}(\sin x+\cos x)^{n-1} \) \( (... |
| 2023-06-09 | Evaluate: \( \int \frac{x^{2}-1}{x \sqrt{x^{4}+4 x^{3}-6 x^{2}+4 x+1}} d x \) |
| 2023-06-09 | If \( I_{m, p}=\int x^{m}\left(a+b x^{n}\right) p \cdot d x \) and \( I_{m, p}=\frac{x^{m+1}\lef... |
| 2023-06-09 | \( \int \frac{e^{x} \sin x \cos x}{(1+\sin x)^{2}(1-\sin x+\cos x)} d x \) is equal to
(a) \( \f... |
| 2023-06-09 | Let \( 4 x^{4}-24 x^{3}+31 x^{2}+6 x-8=0 \) has roots \( \alpha, \beta, \gamma, \delta \), where... |
| 2023-06-09 | Let \( y^{2}=2 x^{2}+4 x+3 \) and \( I_{n}=\int \frac{x^{n}}{y} d x \), then the value of \( a+b... |
| 2023-06-09 | \( \int \frac{\sin ^{3} \frac{\theta}{2} d \theta}{\cos \frac{\theta}{2} \sqrt{\cos ^{3} \theta+... |
| 2023-06-09 | If \( f(x)=\int 2^{\sin x \log _{2} e}\left(\frac{5 \cos x+\cos ^{3} x}{(2-\sin x) \sqrt{3+\cos ... |
| 2023-06-09 | Let \( g(x)=\int \frac{1+2 \cos x}{(\cos x+2)^{2}} d x \) and \( g(0)=0 \) then value of \( g\le... |
| 2023-06-09 | The value of \( \int \frac{x^{2}}{(x \sin x+\cos x)^{2}} \cdot d x \)
(a) \( \frac{-x \sec x}{x ... |
| 2023-06-09 | Let \( f(x) \) satisfies \( x f^{2}(x)-f(x)=x-1 \forall x \in R \) and \( f(1) \neq \) 0 .
If \(... |
| 2023-06-09 | The value of \( \int\left\{\ln (1+\sin x)+x \tan \left(\frac{\pi}{4}-\frac{x}{2}\right)\right\} ... |
| 2023-06-09 | If \( I_{m, n}=\int \sec ^{2 n} x \tan ^{m} x d x, n \geq 1 \) and \( m \geq 2, m, n \in N \), t... |
| 2023-06-09 | (i) \( \int(\sqrt{\cot \theta} \pm \sqrt{\tan \theta}) d \theta \)
(ii) \( \int \frac{\cos x}{\s... |
| 2023-06-09 | If \( g(x)=\left(4 \cos ^{4} x-2 \cos 2 x-\frac{1}{2} \cos 4 x-x^{7}\right)^{\frac{1}{7}} \) the... |
| 2023-06-09 | Evaluate the integration of following inverse trigonometric function:
(i) \( \sin ^{-1} x \)
(ii... |
| 2023-06-09 | Evaluate: \( \int \sqrt{\frac{5-x}{x-2}} d x \) |
| 2023-06-09 | Evaluate: \( \int \tan ^{-1}(\sec x+\tan x) \cdot d x \) is |
0