Advertisements
Advertisements
Question
find `∫_2^4 x/(x^2 + 1)dx`
Advertisements
Solution
`∫_2^4 x/(x^2 + 1)dx`
`Put x^2+1=t`
`2xdx=dt`
Now, `1/2∫_5^17 1/tdt`
`⇒1/2log t_5^17`
`⇒1/2(log 17−log 5)`
`⇒1/2log (17/5)`
APPEARS IN
RELATED QUESTIONS
Evaluate :`int_0^(pi/2)1/(1+cosx)dx`
Evaluate : `int1/(3+5cosx)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 x/(x^2 +1)`dx
Evaluate the integral by using substitution.
`int_0^2 xsqrt(x+2)` (Put x + 2 = `t^2`)
Evaluate the integral by using substitution.
`int_1^2 (1/x- 1/(2x^2))e^(2x) dx`
Evaluate `int_0^(pi/4) (sinx + cosx)/(16 + 9sin2x) dx`
Evaluate of the following integral:
Evaluate of the following integral:
Evaluate the following definite 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 the following integral:
Evaluate
\[\int\limits_0^\pi \frac{x}{1 + \sin \alpha \sin x}dx\]
Evaluate the following integral:
Evaluate : \[\int\limits_{- 2}^1 \left| x^3 - x \right|dx\] .
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_0^(π/2) sin 2x tan^-1 (sin x) dx`.
In Method: Resubstitution, what should be done first?
Which limits are used to evaluate the resulting expression in Method: Resubstitution?
