Advertisements
Advertisements
प्रश्न
Evaluate each of the following integral:
Advertisements
उत्तर
\[\int_0^\frac{\pi}{4} \tan xdx\]
\[ = \left.{\log\sec\ x}\right|_0^\frac{\pi}{4} \]
\[ = \log\sec\frac{\pi}{4} - \log\sec0\]
\[ = \log\sqrt{2} - \log1\]
\[ = \log 2^\frac{1}{2} - 0\]
\[ = \frac{1}{2}\log2\]
APPEARS IN
संबंधित प्रश्न
If f(x) is a continuous function defined on [−a, a], then prove that
Solve each of the following integral:
If \[\int\limits_0^a 3 x^2 dx = 8,\] write the value of a.
\[\int\limits_0^{\pi/2} \frac{1}{1 + \cot^7 x} dx\]
\[\int\limits_0^{\pi/2} \frac{1}{1 + \tan^3 x} dx\]
\[\int\limits_0^\pi \frac{x}{a^2 - \cos^2 x} dx, a > 1\]
\[\int\limits_0^{\pi/2} \frac{dx}{4 \cos x + 2 \sin x}dx\]
Using second fundamental theorem, evaluate the following:
`int_1^"e" ("d"x)/(x(1 + logx)^3`
Evaluate the following using properties of definite integral:
`int_0^(i/2) (sin^7x)/(sin^7x + cos^7x) "d"x`
Evaluate the following using properties of definite integral:
`int_0^1 log (1/x - 1) "d"x`
Evaluate the following integrals as the limit of the sum:
`int_1^3 x "d"x`
Evaluate the following integrals as the limit of the sum:
`int_0^1 x^2 "d"x`
Choose the correct alternative:
Γ(1) is
Evaluate `int (3"a"x)/("b"^2 + "c"^2x^2) "d"x`
