Advertisements
Advertisements
Question
Evaluate:
Advertisements
Solution
\[\int\left( \frac{\cos 2x + 2 \sin^2 x}{\sin^2 x} \right)dx\]
\[ = \int\left( \frac{1 - 2 \sin^2 x + 2 \sin^2 x}{\sin^2 x} \right)dx \left[ \because \cos 2x = 1 - 2 \sin^2 x \right]\]
\[ = \int {cosec}^2\text{ x dx}\]
\[ = - \cot x + C\]
APPEARS IN
RELATED QUESTIONS
Evaluate : `int_0^4(|x|+|x-2|+|x-4|)dx`
Evaluate `∫_0^(3/2)|x cosπx|dx`
Evaluate :
`∫_(-pi)^pi (cos ax−sin bx)^2 dx`
Evaluate :
`∫_0^π(4x sin x)/(1+cos^2 x) dx`
Evaluate :
`int_e^(e^2) dx/(xlogx)`
Evaluate: `intsinsqrtx/sqrtxdx`
Evaluate the integral by using substitution.
`int_0^2 xsqrt(x+2)` (Put x + 2 = `t^2`)
Evaluate of the following integral:
Evaluate of the following integral:
Evaluate:
Evaluate:
Evaluate the following integral:
Evaluate the following integral:
Evaluate the following integral:
Evaluate each of the following integral:
Evaluate each of the following integral:
Evaluate each of the following integral:
Evaluate the following integral:
Evaluate the following integral:
Evaluate :
Evaluate : \[\int\limits_{- 2}^1 \left| x^3 - x \right|dx\] .
Find : \[\int e^{2x} \sin \left( 3x + 1 \right) dx\] .
Find : \[\int\frac{x \sin^{- 1} x}{\sqrt{1 - x^2}}dx\] .
Evaluate: \[\int\limits_0^{\pi/2} \frac{x \sin x \cos x}{\sin^4 x + \cos^4 x}dx\] .
Evaluate: `int_ e^x ((2+sin2x))/cos^2 x dx`
Evaluate: `int_-1^2 (|"x"|)/"x"d"x"`.
Find: `int_ (3"x"+ 5)sqrt(5 + 4"x"-2"x"^2)d"x"`.
`int_0^(pi4) sec^4x "d"x` = ______.
Each student in a class of 40, studies at least one of the subjects English, Mathematics and Economics. 16 study English, 22 Economics and 26 Mathematics, 5 study English and Economics, 14 Mathematics and Economics and 2 study all the three subjects. The number of students who study English and Mathematics but not Economics is
Find: `int (dx)/sqrt(3 - 2x - x^2)`
Evaluate: `int x/(x^2 + 1)"d"x`
