Advertisements
Advertisements
Question
Evaluate:
Advertisements
Solution
\[\int\sqrt{\frac{1 + \cos 2x}{2}}dx\]
\[ \int\sqrt{\frac{\text{2 cos}^2 x}{2}}dx \left[ \therefore 1 + \cos2A = 2 \cos^2 A \right]\]
\[ = \int\ \text{cos x dx}\]
\[ = \sin x + C\]
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 :
`int_e^(e^2) dx/(xlogx)`
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 ______.
`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 definite 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 each of the following integral:
Evaluate the following integral:
Evaluate the following integral:
Evaluate the following integral:
Evaluate the following integral:
Evaluate the following integral:
Evaluate: \[\int\limits_0^{\pi/2} \frac{x \sin x \cos x}{\sin^4 x + \cos^4 x}dx\] .
Evaluate: `int_-π^π (1 - "x"^2) sin "x" cos^2 "x" d"x"`.
Find: `int_ (3"x"+ 5)sqrt(5 + 4"x"-2"x"^2)d"x"`.
`int_0^(pi4) sec^4x "d"x` = ______.
Find: `int (dx)/sqrt(3 - 2x - x^2)`
The value of `int_0^1 (x^4(1 - x)^4)/(1 + x^2) dx` is
If `int x^5 cos (x^6)dx = k sin (x^6) + C`, find the value of k.
