MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Property 1

The value of ...

Question

The value of $\int_{l n 2}^{l n 3} \frac{x s i n x^{2}}{s i n x^{2} + s i n (l n 6 - x^{2})} d x$ is

A

\frac{1}{4} I n \frac{3}{2}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

B

\frac{1}{2} I n \frac{3}{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

C

I n \frac{3}{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

D

\frac{1}{6} I n \frac{3}{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $\frac{1}{4} I n \frac{3}{2}$
$I =$ $\int_{\sqrt{l} n 2}^{\sqrt{l} n 3} \frac{x s i n x^{2}}{s i n x^{2} + s i n (l n 6 - x^{2})} d x$

Put $x^{2} = t$
=> $2 x d x = d t$
The integral will transform into
$I =$ $\int_{l n 2}^{l n 3} \frac{1 / 2 s i n t}{s i n t + s i n (l n 6 - t)} d t$
=> $I =$ $\int_{l n 2}^{l n 3} \frac{1 / 2 s i n (l n 6 - t)}{s i n t + s i n (l n 6 - t)} d t$

Adding both the equations, we get
$2 I =$ $\frac{1}{2}$ $\int_{l n 2}^{l n 3} \frac{s i n t + s i n (l n 6 - t)}{s i n t + s i n (l n 6 - t)} d t$

=> $I =$ $\frac{1}{4}$ $\int_{l n 2}^{l n 3} 1 d t$

=> $I =$ $\frac{1}{4}$ $[l n 3 - l n 2]$

=> $I =$ $\frac{1}{4} l n$ $\frac{3}{2}$

Suggest Corrections

thumbs-up

0

Similar questions

If z = (1 + i $\sqrt{3}$ ).Find the value of ${l o g}_{e}$ z.

Q. Which of the following option correctly represent the correct set of stability order for the given ions?
(I)

G a^{3 +} > I n^{3 +} > T l^{3 +}

G a^{3 +} < I n^{3 +} < T l^{3 +}

G e^{+ 4} > S n^{+ 4} > P b^{+ 4}

G e^{+ 2} < S n^{2 +} < P b^{2 +}

A s^{3 +} < S b^{3 +} < B i^{3 +}

\int_{0}^{2 π} x I n (\frac{3 + c o s x}{3 - c o s x}) d x =

Q. Match the following list

List -I	List -II
(A) $f (x) = x^{2} - 2 x + 5$ is increasing in	1) $ϕ$
(B) $f (x) = e^{- x}$ is increasing in	2) $(- \infty, 1) \cup (2, \infty)$
(C) $f (x) = {log}_{e} x$ is increasing in	3) R
(D) $f (x) = \frac{x^{3}}{3} - \frac{3 x^{2}}{2} + 2 x + 5$ is increasing in	4) $(0, \infty)$
	5) $(1, \infty)$

Q. Consider the following reaction

R C H = C H_{2} + I N_{3}^{⊝} \to A,

A

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Property 1

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon