Mathematics

# If ${ I }_{ n }=\int { { x }^{ n }.{ e }^{ cx } } dx$ for $n\ge 1$, then $c.I_{n}+n.I_{n-1}$ is equal to

$x^{n}e^{cx}$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

#### Realted Questions

Q1 Single Correct Medium
If $\displaystyle f\left ( a+b-x \right )= f\left ( x \right )$ then $\displaystyle \int_{a}^{b}xf\left ( x \right )dx$ is equal to
• A. $\displaystyle \frac{b-a}{2}\int_{a}^{b}f\left ( x \right )dx$
• B. $\displaystyle \frac{a+b}{2}\int_{a}^{b}f\left ( a+b-x \right )dx$
• C. $\displaystyle \frac{a+b}{2}\int_{a}^{b}f\left ( b-x \right )dx$
• D. $\displaystyle \frac{a+b}{2}\int_{a}^{b}f\left ( x \right )dx$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
$\displaystyle \int\frac{x-\sin x}{1-\cos x}dx=$
• A. $log |1-Cosx | +c$
• B. $log | x - sin x | +c$
• C. $x\displaystyle \tan\frac{x}{2}+c$
• D. $-x\displaystyle \cot\frac{x}{2}+c$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Hard
The value of the integral $\int _ { 0 } ^ { \pi / 2 } \frac { 1 + 2 \cos x } { ( 2 + \cos x ) ^ { 2 } } d x$ is
• A. $\frac { 1 } { 4 }$
• B. $\frac { 1 } { 2 }$
• C. $\frac { -1 } { 4 }$
• D. $\frac { -1 } { 2 }$

1 Verified Answer | Published on 17th 09, 2020

Q4 One Word Medium
Solve $\int\limits_{\pi /2}^{3\pi /2} {[2\sin x]dx}$

Given that for each $\displaystyle a \in (0, 1), \lim_{h \rightarrow 0^+} \int_h^{1-h} t^{-a} (1 -t)^{a-1}dt$ exists. Let this limit be $g(a)$
In addition, it is given that the function $g(a)$ is differentiable on $(0, 1)$