_ 4 ^ 2 ( 2 ec , ,x ) ^ 17 ,dx = .......... - Vidyadip

MCQ

$\int\limits_{\frac{\pi }{4}}^{\frac{\pi }{2}} {{{\left( {2\cos ec\,\,x} \right)}^{17}}\,dx = ..........} $

✓
$\int\limits_0^{\log \left( {1 + \sqrt 2 } \right)} {2{{\left( {{e^u} + {e^{ - u}}} \right)}^{16}}du} $
B
$\int\limits_0^{\log \left( {1 + \sqrt 2 } \right)} {{{\left( {{e^u} + {e^{ - u}}} \right)}^{17}}du} $
C
$\int\limits_0^{\log \left( {1 + \sqrt 2 } \right)} {{{\left( {{e^u} - {e^{ - u}}} \right)}^{17}}du} $
D
$\int\limits_0^{\log \left( {1 + \sqrt 2 } \right)} {2{{\left( {{e^u} - {e^{ - u}}} \right)}^{16}}du} $

✓

Answer

Correct option: A.

$\int\limits_0^{\log \left( {1 + \sqrt 2 } \right)} {2{{\left( {{e^u} + {e^{ - u}}} \right)}^{16}}du} $

A

$I=\int_{\frac{\pi}{4}}^{\frac{\pi}{2}} (2\cos ecx)^{17}dx$

$=\int_{\frac{\pi}{4}}^{\frac{\pi}{2}} 2^{17}(2\cos ecx)^{16}\cos ecx \ dx$

અહી,$\cos ecx+\cot x=t$

=$-\cos ecxdx=\frac{dt}{\cos ecx+\cot x}$

તથા

$\begin{cases}x=\frac{\pi}{4}\Rightarrow &t=\sqrt{2}+1\\x=\frac{\pi}{2}\Rightarrow &t=1\end{cases}$

$I=\int_{\sqrt{2}+1}^{'} -2^{17}\left(\frac{t+\frac{1}{t}}{2}\right)^{16}\frac{dt}{t}$

અહી$t=e^u$

$at=e^udu$

$\begin{cases}t=1, & u = 0\\t=\sqrt{2}+1, &u=\log(\sqrt{2}+1)\end{cases}$

$I=-\int_{\log\sqrt{2}+1}^{0} 2(e^u+e^{-u})^{16}\frac{e^udu}{e^u}$.

$I=\int_{\log\sqrt{2}+1}^{0} 2(e^u+e^{-u})^{16}du$

$I=\int_{0}^{\log\sqrt{2}+1} 2(e^u+e^{-u})^{16}du$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "MCQ" from સંકલનનો ઉપયોગ→સંકલનનો ઉપયોગ — all question types→ગણિત ધોરણ 12 સાયન્સ question papers→Gujarat Board ધોરણ 12 સાયન્સ question papers→Gujarat Board question paper generator→

Similar questions

જો $y = x + {1 \over x}$, તો

$\int_{\pi /6}^{\pi /4} {{\rm{cosec}}\,2x\,dx = } $

$\cos ^{-1}(\cos (-5))+\sin ^{-1}(\sin (6))-\tan ^{-1}(\tan (12))$ ની કિમંત મેળવો. (પ્રતિવિધેયની મૂળભૂત કિમંતો ધ્યાનમાં લેવી )

Three coins are tossed. If one of them shows tail, then the probability that all three coins show tail, is

$x+2 y \leq 2, x \geq 0, y \geq 0$ શરતોને આધીન $Z=3 x+2 y$ નું મહતમ કિમત .............. બિંદુ એ થાય.

ગણ $S = \{ x\, \in \,R\,:\,{x^2}\, + \,30\, \le \,11x\} $ પર વિધેય $f\,(x)\, = 3{x^3} - 18{x^2} + 27x\,\, - 40$ ની મહતમ કિમંત મેળવો.

$\int_{\,0}^{\,3} {\,\frac{{3x + 1}}{{{x^2} + 9}}dx = } $

જો $\int\limits_0^{\frac{\pi }{3}} {\frac{{\tan \,\,\theta }}{{\sqrt {2k\,\sec \,\theta } }}} \,d\theta \, = \,1 - \frac{1}{{\sqrt 2 }},(k > 0),$ તો $k$ ની કિમંત મેળવો.

જો $f : [2,\infty]\ \rightarrow R,f(x)=x^2-4x+5$ હોય તો $f$ ના વિસ્તારનો ન્યૂનતમ ઘટક $....$ છે.

ગણ $\left\{A=\left(\begin{array}{ll}a & b \\ 0 & d\end{array}\right): a, b, d \in\{-1,0,1\}\right.$ અને $\left.(I-A)^{3}=I-A^{3}\right\}$ ની સભ્ય સંખ્યા મેળવો. કે જ્યાં $I$ એ $2 \times 2$ એકમ શ્રેણિક છે.