Advertisements
Advertisements
Question
Find: `int (dx)/sqrt(3 - 2x - x^2)`
Advertisements
Solution
`int (dx)/sqrt(3 - 2x - x^2) = int (dx)/sqrt(-(x^2 + 2x - 3))`
= `int (dx)/sqrt(4 - (x + 1)^2`
= `sin^-1 ((x + 1)/2) + C` .....`[int (dx)/sqrt(a^2 - x^2) = sin^-1 (x/a) + C]`
APPEARS IN
RELATED QUESTIONS
Evaluate: `int (1+logx)/(x(2+logx)(3+logx))dx`
Evaluate :`int_0^(pi/2)1/(1+cosx)dx`
Evaluate : `int1/(3+5cosx)dx`
Evaluate `∫_0^(3/2)|x cosπx|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`
Evaluate the integral by using substitution.
`int_0^(pi/2) (sin x)/(1+ cos^2 x) dx`
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 of the following integral:
Evaluate of the following integral:
Evaluate:
Evaluate:
Evaluate the following definite 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 the following integral:
`int_0^1 x(1 - x)^5 "dx" =` ______.
`int_0^(pi4) sec^4x "d"x` = ______.
Evaluate: `int_0^(π/2) sin 2x tan^-1 (sin x) dx`.
