Advertisements
Advertisements
प्रश्न
Advertisements
उत्तर
\[\int_0^4 \frac{1}{\sqrt{16 - x^2}} d x\]
\[ = \int_0^4 \frac{1}{\sqrt{4^2 - x^2}} d x\]
\[ = \left[ \sin^{- 1} \frac{x}{4} \right]_0^4 \]
\[ = \left( \frac{\pi}{2} - 0 \right)\]
\[ = \frac{\pi}{2}\]
APPEARS IN
संबंधित प्रश्न
\[\int\limits_{\pi/4}^{\pi/2} \cot x\ dx\]
If f is an integrable function, show that
If f (x) is a continuous function defined on [0, 2a]. Then, prove that
Evaluate each of the following integral:
If \[\int\limits_0^a 3 x^2 dx = 8,\] write the value of a.
The value of \[\int\limits_0^\pi \frac{x \tan x}{\sec x + \cos x} dx\] is __________ .
If \[I_{10} = \int\limits_0^{\pi/2} x^{10} \sin x\ dx,\] then the value of I10 + 90I8 is
\[\int\limits_1^2 \frac{1}{x^2} e^{- 1/x} dx\]
Evaluate the following integrals :-
\[\int_2^4 \frac{x^2 + x}{\sqrt{2x + 1}}dx\]
\[\int\limits_{- a}^a \frac{x e^{x^2}}{1 + x^2} dx\]
\[\int\limits_0^{\pi/2} \frac{1}{2 \cos x + 4 \sin x} dx\]
Find : `∫_a^b logx/x` dx
Evaluate `int sqrt((1 + x)/(1 - x)) "d"x`, x ≠1
If `int (3"e"^x - 5"e"^-x)/(4"e"6x + 5"e"^-x)"d"x` = ax + b log |4ex + 5e –x| + C, then ______.
Verify the following:
`int (2x + 3)/(x^2 + 3x) "d"x = log|x^2 + 3x| + "C"`
Given `int "e"^"x" (("x" - 1)/("x"^2)) "dx" = "e"^"x" "f"("x") + "c"`. Then f(x) satisfying the equation is:
