Advertisements
Advertisements
प्रश्न
Advertisements
उत्तर
\[ = \sqrt{2} \int_\pi^\frac{3\pi}{2} \left| \sin x \right|dx\]
\[ = - \sqrt{2} \int_\pi^\frac{3\pi}{2} \sin x\ dx .................\left( \sin x < 0 for\ \pi \leq x \leq 2\pi \right)\]
\[= - \sqrt{2}\left( - \cos x \right) |_\pi^\frac{3\pi}{2} \]
\[ = \sqrt{2}\left( \cos\frac{3\pi}{2} - cos\pi \right)\]
\[ = \sqrt{2} \left[ 0 - \left( - 1 \right) \right]\]
\[ = \sqrt{2} \times 1\]
\[ = \sqrt{2}\]
APPEARS IN
संबंधित प्रश्न
Prove that: `int_0^(2a)f(x)dx=int_0^af(x)dx+int_0^af(2a-x)dx`
If `int_0^alpha3x^2dx=8` then the value of α is :
(a) 0
(b) -2
(c) 2
(d) ±2
By using the properties of the definite integral, evaluate the integral:
`int_0^pi log(1+ cos x) dx`
By using the properties of the definite integral, evaluate the integral:
`int_0^4 |x - 1| dx`
Evaluate `int e^x [(cosx - sin x)/sin^2 x]dx`
\[\int\limits_0^a 3 x^2 dx = 8,\] find the value of a.
Evaluate : `int 1/("x" [("log x")^2 + 4]) "dx"`
Evaluate : `int 1/sqrt("x"^2 - 4"x" + 2) "dx"`
Using properties of definite integrals, evaluate
`int_0^(π/2) sqrt(sin x )/ (sqrtsin x + sqrtcos x)dx`
Prove that `int_0^"a" "f" ("x") "dx" = int_0^"a" "f" ("a" - "x") "d x",` hence evaluate `int_0^pi ("x" sin "x")/(1 + cos^2 "x") "dx"`
`int_0^2 e^x dx` = ______.
`int_1^2 1/(2x + 3) dx` = ______
`int_0^4 1/(1 + sqrtx)`dx = ______.
`int_-9^9 x^3/(4 - x^2)` dx = ______
If f(x) = |x - 2|, then `int_-2^3 f(x) dx` is ______
The value of `int_1^3 dx/(x(1 + x^2))` is ______
`int_0^1 "dx"/(sqrt(1 + x) - sqrtx)` = ?
`int_0^pi x*sin x*cos^4x "d"x` = ______.
`int_0^9 1/(1 + sqrtx)` dx = ______
`int_(-1)^1 (x^3 + |x| + 1)/(x^2 + 2|x| + 1) "d"x` is equal to ______.
`int_(-2)^2 |x cos pix| "d"x` is equal to ______.
`int_0^(pi/2) (sin^"n" x"d"x)/(sin^"n" x + cos^"n" x)` = ______.
If `f(a + b - x) = f(x)`, then `int_0^b x f(x) dx` is equal to
`int_0^1 1/(2x + 5) dx` = ______.
Let a be a positive real number such that `int_0^ae^(x-[x])dx` = 10e – 9 where [x] is the greatest integer less than or equal to x. Then, a is equal to ______.
The value of `int_((-1)/sqrt(2))^(1/sqrt(2)) (((x + 1)/(x - 1))^2 + ((x - 1)/(x + 1))^2 - 2)^(1/2)`dx is ______.
If `lim_("n"→∞)(int_(1/("n"+1))^(1/"n") tan^-1("n"x)"d"x)/(int_(1/("n"+1))^(1/"n") sin^-1("n"x)"d"x) = "p"/"q"`, (where p and q are coprime), then (p + q) is ______.
`int_((-π)/2)^(π/2) log((2 - sinx)/(2 + sinx))` is equal to ______.
Evaluate `int_0^(π//4) log (1 + tanx)dx`.
If `int_0^(2π) cos^2 x dx = k int_0^(π/2) cos^2 x dx`, then the value of k is ______.
Assertion (A): `int_2^8 sqrt(10 - x)/(sqrt(x) + sqrt(10 - x))dx` = 3.
Reason (R): `int_a^b f(x) dx = int_a^b f(a + b - x) dx`.
Evaluate the following definite integral:
`int_4^9 1/sqrt"x" "dx"`
`int_1^2 x logx dx`= ______
Evaluate the following integral:
`int_0^1x(1 - x)^5dx`
Solve the following.
`int_0^1e^(x^2)x^3dx`
`int_0^(pi/4) (cos^2 x)/(cos^2 x + 4 sin^2 x) dx` =
What is the value of a definite integral when its upper and lower limits are equal?
Which formula is \[P_5\] : Halving the Upper Limit (Addition)?
What is the value of \[\int_{-\frac{\pi}{4}}^{\frac{\pi}{4}}\sin^{2}x\,dx\]?
