Advertisements
Advertisements
प्रश्न
Evaluate the integral by using substitution.
`int_0^(pi/2) (sin x)/(1+ cos^2 x) dx`
Advertisements
उत्तर
`int_0^(pi/2) (sin x)/(1 + cos^2 x) ` dx
Substituting cos x = t,
⇒ - sin x dx = dt
And x = 0, t = 1, x `= pi/2,` t = 0
Hence, `I = - int_1^0 1/(1 + t^2)` dt
`= - [tan^-1 t]_1^0`
`= - [tan^-1 0 - tan^-1 1]`
`= - [0 - pi/4]`
`= pi/4`
APPEARS IN
संबंधित प्रश्न
Evaluate :
`∫_(-pi)^pi (cos ax−sin bx)^2 dx`
find `∫_2^4 x/(x^2 + 1)dx`
If `int_0^a1/(4+x^2)dx=pi/8` , find the value of a.
Evaluate the integral by using substitution.
`int_1^2 (1/x- 1/(2x^2))e^(2x) dx`
The value of the integral `int_(1/3)^4 ((x- x^3)^(1/3))/x^4` dx is ______.
If `f(x) = int_0^pi t sin t dt`, then f' (x) is ______.
`int 1/(1 + cos x)` dx = _____
A) `tan(x/2) + c`
B) `2 tan (x/2) + c`
C) -`cot (x/2) + c`
D) -2 `cot (x/2)` + c
Evaluate of the following integral:
Evaluate:
Evaluate:
Evaluate the following integral:
Evaluate the following integral:
\[\int\limits_0^2 \left| x^2 - 3x + 2 \right| dx\]
Evaluate the following integral:
Evaluate the following integral:
Evaluate the following integral:
Evaluate the following integral:
Evaluate the following integral:
Evaluate the following integral:
Evaluate the following integral:
Evaluate
\[\int\limits_0^\pi \frac{x}{1 + \sin \alpha \sin x}dx\]
Find : \[\int\frac{x \sin^{- 1} x}{\sqrt{1 - x^2}}dx\] .
Evaluate: `int_-π^π (1 - "x"^2) sin "x" cos^2 "x" d"x"`.
Evaluate: `int_-1^2 (|"x"|)/"x"d"x"`.
Evaluate: `int_1^5{|"x"-1|+|"x"-2|+|"x"-3|}d"x"`.
Find: `int_ (3"x"+ 5)sqrt(5 + 4"x"-2"x"^2)d"x"`.
`int_(pi/5)^((3pi)/10) [(tan x)/(tan x + cot x)]`dx = ?
If `I_n = int_0^(pi/4) tan^n theta "d"theta " then " I_8 + I_6` equals ______.
Find: `int (dx)/sqrt(3 - 2x - x^2)`
`int_0^1 x^2e^x dx` = ______.
If `int x^5 cos (x^6)dx = k sin (x^6) + C`, find the value of k.
After finding the antiderivative in Method: Resubstitution, what is the next step?
If the substitution is \[t=g(x)\], what differential relation is used in Method 2: Changing the Limits?
What is the value of \[\int_{0}^{1}\frac{\tan^{-1}x}{1+x^2}\,dx\]?
What should not be added in a definite integral?
