If ∫01x^11e^(-x24)dx=A, and ∫01x^3e^(-x8)dx=B, then the relation between A and B is

Correct answer: (B) B=3A. In A, let x^12=t ⇒12x^11dx=dt ⇒A=1/12∫01e^(-t2)dt In B, let x^4=u ⇒4x^3dx=du ⇒B=1/4∫01e^(-u2)dx=1/4∫01e^(-t2)dt ⇒B=1/412A⇒B=3A

Q29 / 116 · NTA Abhyas (JEE Main) 2020 · Mathematics · Definite Integration

If $\int_{0}^{1} x^{11} e^{- x^{24}} d x = A,$ and $\int_{0}^{1} x^{3} e^{- x^{8}} d x = B,$ then the relation between $A$ and $B$ is

A
$A = 3 B$
Correct answer
B
$B = 3 A$
C
$A + 3 B = 0$
D
$B + 3 A = 0$

Solution

A,

let

x^{12} = t

\Rightarrow 12 x^{11} d x = d t

\Rightarrow A = \frac{1}{12} \int_{0}^{1} e^{- t^{2}} d t

B,

let

x^{4} = u

\Rightarrow 4 x^{3} d x = d u

\Rightarrow B = \frac{1}{4} \int_{0}^{1} e^{- u^{2}} d x = \frac{1}{4} \int_{0}^{1} e^{- t^{2}} d t

\Rightarrow B = \frac{1}{4} (12 A) \Rightarrow B = 3 A

Hence, the correct answer is option: 'B'.

If ∫01x11e-x24dx=A, and ∫01x3e-x8dx=B, then the relation between A and B is

Solution

More Definite Integration Questions

If $\int_{0}^{1} x^{11} e^{- x^{24}} d x = A,$ and $\int_{0}^{1} x^{3} e^{- x^{8}} d x = B,$ then the relation between $A$ and $B$ is