Advertisements
Advertisements
Question
Solution
\[\int_0^\frac{\pi}{4} \tan^2 x\ d x\]
\[ = \int_0^\frac{\pi}{4} \left( se c^2 x - 1 \right) d x\]
\[ = \left[ \tan x - x \right]_0^\frac{\pi}{4} \]
\[ = 1 - \frac{\pi}{4} - 0\]
\[ = 1 - \frac{\pi}{4}\]
APPEARS IN
RELATED QUESTIONS
If `f` is an integrable function such that f(2a − x) = f(x), then prove that
Evaluate each of the following integral:
Evaluate :
\[\int\limits_0^\pi \frac{1}{1 + \sin x} dx\] equals
\[\int\limits_0^\infty \frac{1}{1 + e^x} dx\] equals
\[\int\limits_0^\infty \frac{x}{\left( 1 + x \right)\left( 1 + x^2 \right)} dx\]
\[\int\limits_1^2 \frac{x + 3}{x\left( x + 2 \right)} dx\]
\[\int\limits_0^{\pi/2} \frac{1}{2 \cos x + 4 \sin x} dx\]
\[\int\limits_0^4 x dx\]
\[\int\limits_0^2 \left( x^2 + 2 \right) dx\]
Prove that `int_a^b ƒ ("x") d"x" = int_a^bƒ(a + b - "x") d"x" and "hence evaluate" int_(π/6)^(π/3) (d"x")/(1+sqrt(tan "x")`
Evaluate the following using properties of definite integral:
`int_0^(i/2) (sin^7x)/(sin^7x + cos^7x) "d"x`
Evaluate the following integrals as the limit of the sum:
`int_0^1 (x + 4) "d"x`
Choose the correct alternative:
`Γ(3/2)`
