The value of \( \int_{0}^{\pi / 16}\left(\frac{\sin x+\sin 2 x+\sin 3 x+\ldots \ldots+\sin 7 x}{...
The value of \( \int_{0}^{\pi / 16}\left(\frac{\sin x+\sin 2 x+\sin 3 x+\ldots \ldots+\sin 7 x}{\cos x+\cos 2 x+\cos 3 x+\ldots \ldots+\cos 7 x}\right) d x \)
(a) \( \frac{1}{8} \ln 2 \)
(b) \( 8 \ln 2 \)
(c) \( 2 \ln 8 \)
(d) \( \frac{1}{2} \ln 8 \)
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live
Other Videos By PW Solutions
| 2023-06-09 | If \( z_{1}, z_{2}, z_{3} \) are the affixes of vertices of an equilateral triangle, then \( \in... |
| 2023-06-09 | \[
\int_{0}^{1000} e^{x-[x]} d x
\]
(a) \( 1000(e+1) \)
(b) \( 1000(e-1) \)
(c) \( 100(e+2) \)
(... |
| 2023-06-09 | Find the indefinite integral \( \int\left(\frac{1}{\sqrt[3]{x}+\sqrt[4]{x}}+\frac{\ln (1+\sqrt[6... |
| 2023-06-09 | \[
\int_{-x / 2}^{x / 2} \sqrt{\cos ^{2021} x-\cos ^{2023} x} d x
\]
(a) \( \frac{2}{2023} \)
(b... |
| 2023-06-09 | Evaluate \( \int_{0}^{1} \sqrt[2022]{1-x^{2023}} d x+\int_{1}^{0} \sqrt[2023]{1-x^{2022}} d x \)... |
| 2023-06-09 | Evaluate \( \int_{-1}^{1}\left(\frac{d}{d x}\left(\frac{1}{1+e^{1 / x}}\right)\right) d x \)
(a)... |
| 2023-06-09 | Value of the definite integral
\[
\int_{-1 / 2}^{1 / 2}\left(\sin ^{-1}\left(3 x-4 x^{3}\right)-... |
| 2023-06-09 | The value of the integral \( \int_{-1}^{3}\left(\tan ^{-1} \frac{x}{x^{2}+1}+\tan ^{-1} \frac{x^... |
| 2023-06-09 | The value of \( \int_{0+}^{1} \frac{x^{x}\left(x^{2 x}+1\right)(\ln x+1)}{x^{4 x}+1} d x \)
(a) ... |
| 2023-06-09 | The value of \( \int_{0}^{2}\left[x^{2}-x+1\right] d x \), where [.] denotes greatest integer fu... |
| 2023-06-09 | The value of \( \int_{0}^{\pi / 16}\left(\frac{\sin x+\sin 2 x+\sin 3 x+\ldots \ldots+\sin 7 x}{... |
| 2023-06-09 | If \( \int_{a}^{b}|\sin x| d x=8 \& \int_{0}^{a+b}|\cos x| d x=9 \) then;
(a) \( a+b=9 \pi \)
(b... |
| 2023-06-09 | Find the indefinite integral
\[
\int \cos 2 \theta \ln \left(\frac{\cos \theta+\sin \theta}{\cos... |
| 2023-06-09 | The value of \( \int_{a}^{b} \frac{|x|}{x} d x \)
(a) \( b-a \)
(b) \( |b|-|a| \)
(c) \( |b|+|a|... |
| 2023-06-09 | The value of \( \int_{0}^{\infty} x^{2 n+1} e^{-x^{2}} d x, n \in N \)
(a) \( n ! \)
(b) \( (n+1... |
| 2023-06-09 | Assume that \( f^{\prime \prime} \) is continuous and that \( f(1)=3, f^{\prime}(1)=2 \) and \( ... |
| 2023-06-09 | Evaluate \( \int \sin ^{-1}\left(\frac{2 x+2}{\sqrt{4 x^{2}+8 x+13}}\right) d x \) |
| 2023-06-09 | Evaluate \( \int\left(x^{3 m}+x^{2 m}+x^{m}\right)\left(2 x^{2 m}+3 x^{m}+6\right)^{1 / m} d x, ... |
| 2023-06-09 | If \( g(x) \) is the inverse of \( f(x) \) and \( f(x) \) has domain \( x \in[1,5] \), where \( ... |
| 2023-06-09 | For \( I(x)=\int \frac{\sec ^{2} x-2022}{\sin ^{2022} x} d x \), if \( I\left(\frac{\pi}{4}\righ... |
| 2023-06-09 | \[
\int_{-\pi / 2}^{\pi / 2} \log \left(\frac{2-\sin \theta}{2+\sin \theta}\right) d \theta=
\]
... |
0