Advertisements
Advertisements
प्रश्न
Evaluate the following:
f(x) = `{{:("c"x",", 0 < x < 1),(0",", "otherwise"):}` Find 'c" if `int_0^1 "f"(x) "d"x` = 2
बेरीज
Advertisements
उत्तर
f(x) = `{{:("c"x",", 0 < x < 1),(0",", "otherwise"):}`
⇒ `int_0^1 "f"(x) "d"x` = 2
⇒ `int_0^2 "c"x "d"x` = 2
`"c"[x^2/2]_0^1` = 2
`"c"[1/2 - 0]` = 2
`1/2` = 2
⇒ c = 4
shaalaa.com
Definite Integrals
या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
APPEARS IN
संबंधित प्रश्न
\[\int\limits_0^{\pi/2} \frac{\sin x \cos x}{1 + \sin^4 x} dx\]
\[\int_0^\frac{1}{2} \frac{x \sin^{- 1} x}{\sqrt{1 - x^2}}dx\]
\[\int\limits_0^{\pi/2} \sin 2x \tan^{- 1} \left( \sin x \right) dx\]
\[\int\limits_0^5 \frac{\sqrt[4]{x + 4}}{\sqrt[4]{x + 4} + \sqrt[4]{9 - x}} dx\]
\[\int_0^1 | x\sin \pi x | dx\]
\[\int\limits_1^4 \left( x^2 - x \right) dx\]
\[\int\limits_0^2 \left( x^2 + 2x + 1 \right) dx\]
\[\int\limits_0^{\pi/2} x \sin x\ dx\] is equal to
\[\int\limits_0^\pi \frac{x}{1 + \cos \alpha \sin x} dx\]
Choose the correct alternative:
If n > 0, then Γ(n) is
