Advertisements
Advertisements
प्रश्न
`int_0^(pi/2) cos x "e"^(sinx) "d"x` is equal to ______.
Advertisements
उत्तर
`int_0^(pi/2) cos x "e"^(sinx) "d"x` is equal to e – 1.
Explanation:
Let I = `int_0^(pi/2) cos x "e"^(sinx) "d"x`
Put sin x = t
⇒ cos x "d"x` = dt
∴ I = `int_0^1 "e"^"t" "dt"`
= `["e"^"t"]_0^1`
= `"e"^1 - "e"^0`
= e – 1
APPEARS IN
संबंधित प्रश्न
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_(-5)^5 | x + 2| dx`
By using the properties of the definite integral, evaluate the integral:
`int_0^2 xsqrt(2 -x)dx`
By using the properties of the definite integral, evaluate the integral:
`int_0^pi log(1+ cos x) dx`
Show that `int_0^a f(x)g (x)dx = 2 int_0^a f(x) dx` if f and g are defined as f(x) = f(a-x) and g(x) + g(a-x) = 4.
`int_(-pi/2)^(pi/2) (x^3 + x cos x + tan^5 x + 1) dx ` is ______.
Evaluate `int_0^(pi/2) cos^2x/(1+ sinx cosx) dx`
\[\int\limits_0^k \frac{1}{2 + 8 x^2} dx = \frac{\pi}{16},\] find the value of k.
Evaluate the following integral:
`int_0^1 x(1 - x)^5 *dx`
`int_2^7 sqrt(x)/(sqrt(x) + sqrt(9 - x)) dx` = ______.
Evaluate `int_1^3 x^2*log x "d"x`
`int_0^(pi/2) sqrt(cos theta) * sin^2 theta "d" theta` = ______.
`int_-2^1 dx/(x^2 + 4x + 13)` = ______
`int_{pi/6}^{pi/3} sin^2x dx` = ______
`int_(-1)^1 log ((2 - x)/(2 + x)) "dx" = ?`
The value of `int_2^7 (sqrtx)/(sqrt(9 - x) + sqrtx)dx` is ______
`int_0^(pi/2) 1/(1 + cos^3x) "d"x` = ______.
Find `int_2^8 sqrt(10 - x)/(sqrt(x) + sqrt(10 - x)) "d"x`
Evaluate `int_(-1)^2 "f"(x) "d"x`, where f(x) = |x + 1| + |x| + |x – 1|
If `int (log "x")^2/"x" "dx" = (log "x")^"k"/"k" + "c"`, then the value of k is:
`int_0^(2"a") "f"("x") "dx" = int_0^"a" "f"("x") "dx" + int_0^"a" "f"("k" - "x") "dx"`, then the value of k is:
`int_a^b f(x)dx = int_a^b f(x - a - b)dx`.
If `β + 2int_0^1x^2e^(-x^2)dx = int_0^1e^(-x^2)dx`, then the value of β is ______.
For any integer n, the value of `int_-π^π e^(cos^2x) sin^3 (2n + 1)x dx` is ______.
Evaluate the following limit :
`lim_("x"->3)[sqrt("x"+6)/"x"]`
Evaluate the following definite integral:
`int_4^9 1/sqrt"x" "dx"`
Solve the following.
`int_1^3 x^2 logx dx`
`int_1^2 x logx dx`= ______
Evaluate: `int_-1^1 x^17.cos^4x dx`
Evaluate:
`int_0^1 |2x + 1|dx`
Evaluate the following integral:
`int_0^1 x(1 - x)^5 dx`
Solve the following.
`int_2^3x/((x+2)(x+3))dx`
Solve the following.
`int_0^1e^(x^2)x^3dx`
Evaluate the following definite intergral:
`int_1^2 (3x)/(9x^2 - 1) dx`
Evaluate the following definite integral:
`int_-2^3(1)/(x + 5) dx`
`∫_0^(π/2) (sqrttan x + sqrtcot x)dx` = ______.
The area enclosed between the graph of y = x3 and the lines x = 0, y = 1, y = 8 is ______.
