Advertisements
Advertisements
प्रश्न
Advertisements
उत्तर
\[Let I = \int_4^9 \frac{1}{\sqrt{x}} d x . Then, \]
\[I = 2 \int_4^9 \frac{1}{2\sqrt{x}} d x\]
\[ \Rightarrow I = 2 \left[ \sqrt{x} \right]_4^9 \]
\[ \Rightarrow I = 2\left( 3 - 2 \right)\]
\[ \Rightarrow I = 2\]
APPEARS IN
संबंधित प्रश्न
Evaluate the following definite integrals:
Evaluate the following integral:
If f(2a − x) = −f(x), prove that
If \[\int_0^a \frac{1}{4 + x^2}dx = \frac{\pi}{8}\] , find the value of a.
\[\int_0^\frac{\pi^2}{4} \frac{\sin\sqrt{x}}{\sqrt{x}} dx\] equals
The value of \[\int\limits_0^{\pi/2} \log\left( \frac{4 + 3 \sin x}{4 + 3 \cos x} \right) dx\] is
Evaluate: \[\int\limits_{- \pi/2}^{\pi/2} \frac{\cos x}{1 + e^x}dx\] .
\[\int\limits_1^5 \frac{x}{\sqrt{2x - 1}} dx\]
\[\int\limits_0^\pi \sin^3 x\left( 1 + 2 \cos x \right) \left( 1 + \cos x \right)^2 dx\]
\[\int\limits_0^1 \left| 2x - 1 \right| dx\]
\[\int\limits_0^{2\pi} \cos^7 x dx\]
\[\int\limits_2^3 \frac{\sqrt{x}}{\sqrt{5 - x} + \sqrt{x}} dx\]
\[\int\limits_0^{\pi/2} \frac{1}{2 \cos x + 4 \sin x} dx\]
\[\int\limits_0^4 x dx\]
Choose the correct alternative:
`int_(-1)^1 x^3 "e"^(x^4) "d"x` is
Integrate `((2"a")/sqrt(x) - "b"/x^2 + 3"c"root(3)(x^2))` w.r.t. x
Verify the following:
`int (x - 1)/(2x + 3) "d"x = x - log |(2x + 3)^2| + "C"`
Evaluate \[\int_{1}^{3}(2x+1)\,dx\].
