Mathematics

# $\displaystyle\int^b_a\cos x dx$Obtain the definite integral as a limit of d sum.

##### SOLUTION
$\displaystyle \int^b_a \cos x dx$
$\cos b - \cos a$
$\displaystyle \sum_{k=0}^{k=\infty} \cfrac{(-1)^k (b^{2k}-a^{2k})}{2k!}$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

#### Realted Questions

Q1 One Word Medium
$\displaystyle \int_{0}^{\pi /4}\sqrt{\tan \Theta} d\Theta =\frac{1}{\sqrt{(2)}}log(\sqrt{2}-1)+\frac{\pi }{2k\sqrt{(2)}}$.Find the value of $k$.

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
Evaluate the integral
$\displaystyle \int_{0}^{\pi /4}\frac{ {x}^{2} {d} {x}}{( {x} {si} {n} {x}+ {c} {o} {s} {x})^{2}}$
• A. $\displaystyle \dfrac{4+\pi}{4-\pi}$
• B. $\displaystyle \dfrac{4+\pi}{2(4-\pi)}$
• C. $2\left[\displaystyle \dfrac{4-\pi}{4+\pi}\right]$
• D. $\displaystyle \dfrac{4-\pi}{4+\pi}$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Hard
The value of the integral $\displaystyle \int_{0}^{\pi/4}\dfrac {\sin x + \cos x}{3 + \sin 2x}dx$ is equal to
• A. $\log_{e}2$
• B. $\log_{e}3$
• C. $\dfrac {1}{4}\log_{e} 2$
• D. $\dfrac {1}{4}\log_{e} 3$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Evaluate the following integral:
$\displaystyle \int { \sqrt { x } \left( { x }^{ 3 }-\cfrac { 2 }{ x } \right) } dx\quad$

1 Verified Answer | Published on 17th 09, 2020

Q5 Subjective Medium
$\int \frac{1}{1+x}\;dx$