Advertisements
Advertisements
प्रश्न
Evaluate the integral by using substitution.
`int_0^1 x/(x^2 +1)`dx
Advertisements
उत्तर
Let `int_0^1 x/(x^2 + 1) dx`
Put x2 + 1 = t
2x dx = dt
When x =1, t = 2; x = 0, t = 1
`therefore I = int_1^2 dt/t`
∴ `I = 1/2 int_1^2 dt/t = [1/2 log t]_1^2`
`= 1/2 [log 2 - log 1]`
`= 1/2 log 2`
APPEARS IN
संबंधित प्रश्न
Evaluate :`int_0^(pi/2)1/(1+cosx)dx`
Evaluate `∫_0^(3/2)|x cosπx|dx`
Evaluate `int_(-1)^2|x^3-x|dx`
Evaluate :
`∫_0^π(4x sin x)/(1+cos^2 x) dx`
If `int_0^a1/(4+x^2)dx=pi/8` , find the value of a.
Evaluate the integral by using substitution.
`int_0^1 sin^(-1) ((2x)/(1+ x^2)) 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 ______.
Evaluate of the following integral:
Evaluate of the following integral:
Evaluate of the following integral:
Evaluate :
Evaluate:
Evaluate:
Evaluate the following integral:
Evaluate the following integral:
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 each of the following integral:
Evaluate the following integral:
Evaluate the following integral:
Evaluate :
Evaluate: `int_1^5{|"x"-1|+|"x"-2|+|"x"-3|}d"x"`.
`int_0^1 x(1 - x)^5 "dx" =` ______.
`int_0^(pi4) sec^4x "d"x` = ______.
Evaluate the following:
`int ("e"^(6logx) - "e"^(5logx))/("e"^(4logx) - "e"^(3logx)) "d"x`
Evaluate the following:
`int "dt"/sqrt(3"t" - 2"t"^2)`
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`
