Advertisements
Advertisements
प्रश्न
Advertisements
उत्तर
\[Let\ I = \int_0^\frac{\pi}{2} \left( \sin x + \cos x \right) d x . Then, \]
\[I = \left[ - \cos x + \sin x \right]_0^\frac{\pi}{2} \]
\[ \Rightarrow I = 0 + 1 - \left( - 1 + 0 \right)\]
\[ \Rightarrow I = 2\]
APPEARS IN
संबंधित प्रश्न
If f(2a − x) = −f(x), prove that
Prove that:
\[\int\limits_0^{\pi/2} \frac{1}{2 + \cos x} dx\] equals
The value of \[\int\limits_{- \pi}^\pi \sin^3 x \cos^2 x\ dx\] is
Evaluate : \[\int\limits_0^\pi/4 \frac{\sin x + \cos x}{16 + 9 \sin 2x}dx\] .
\[\int\limits_1^5 \frac{x}{\sqrt{2x - 1}} dx\]
\[\int\limits_0^1 \tan^{- 1} x dx\]
\[\int\limits_1^2 \frac{1}{x^2} e^{- 1/x} dx\]
Evaluate the following integrals :-
\[\int_2^4 \frac{x^2 + x}{\sqrt{2x + 1}}dx\]
\[\int\limits_0^{\pi/2} \frac{dx}{4 \cos x + 2 \sin x}dx\]
Evaluate the following:
`int_(-1)^1 "f"(x) "d"x` where f(x) = `{{:(x",", x ≥ 0),(-x",", x < 0):}`
Evaluate the following:
f(x) = `{{:("c"x",", 0 < x < 1),(0",", "otherwise"):}` Find 'c" if `int_0^1 "f"(x) "d"x` = 2
Evaluate the following using properties of definite integral:
`int_0^(i/2) (sin^7x)/(sin^7x + cos^7x) "d"x`
Choose the correct alternative:
`int_0^oo "e"^(-2x) "d"x` is
Evaluate `int (x^2"d"x)/(x^4 + x^2 - 2)`
Evaluate: `int_(-1)^2 |x^3 - 3x^2 + 2x|dx`
