Advertisements
Advertisements
प्रश्न
`∫_4^9 1/sqrtxdx=`_____
(A) 1
(B) –2
(C) 2
(D) –1
उत्तर
Let `I=∫_4^9 1/sqrtxdx`
`=∫_4^9 x^-(1/2)dx`
`=[x^(1/2)/(1/2)]_4^9=2[sqrtx]_4^9`
`=2(sqrt9-sqrt4)`
`=2(3-2)`
`therefore I=2`
APPEARS IN
संबंधित प्रश्न
Evaluate :`int_0^pi(xsinx)/(1+sinx)dx`
By using the properties of the definite integral, evaluate the integral:
`int_0^(pi/2) (2log sin x - log sin 2x)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 e^x [(cosx - sin x)/sin^2 x]dx`
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 : ∫ log (1 + x2) dx
Evaluate the following integrals : `int_2^5 sqrt(x)/(sqrt(x) + sqrt(7 - x))*dx`
`int_0^2 e^x dx` = ______.
`int_1^2 1/(2x + 3) dx` = ______
`int_(-7)^7 x^3/(x^2 + 7) "d"x` = ______
State whether the following statement is True or False:
`int_(-5)^5 x/(x^2 + 7) "d"x` = 10
`int_0^1 (1 - x/(1!) + x^2/(2!) - x^3/(3!) + ... "upto" ∞)` e2x dx = ?
`int_0^{pi/2} log(tanx)dx` = ______
`int_(pi/18)^((4pi)/9) (2 sqrt(sin x))/(sqrt (sin x) + sqrt(cos x))` dx = ?
f(x) = `{:{(x^3/k; 0 ≤ x ≤ 2), (0; "otherwise"):}` is a p.d.f. of X. The value of k is ______
`int_0^1 "dx"/(sqrt(1 + x) - sqrtx)` = ?
`int_0^pi sin^2x.cos^2x dx` = ______
`int_(-pi/4)^(pi/4) 1/(1 - sinx) "d"x` = ______.
Find `int_2^8 sqrt(10 - x)/(sqrt(x) + sqrt(10 - x)) "d"x`
`int_("a" + "c")^("b" + "c") "f"(x) "d"x` is equal to ______.
If `int_0^1 "e"^"t"/(1 + "t") "dt"` = a, then `int_0^1 "e"^"t"/(1 + "t")^2 "dt"` is equal to ______.
Evaluate the following:
`int_(-pi/4)^(pi/4) log|sinx + cosx|"d"x`
`int_0^(pi/2) sqrt(1 - sin2x) "d"x` is equal to ______.
`int_a^b f(x)dx` = ______.
The value of the integral `int_(-1)^1log_e(sqrt(1 - x) + sqrt(1 + x))dx` is equal to ______.
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 ______.
If f(x) = `(2 - xcosx)/(2 + xcosx)` and g(x) = logex, (x > 0) then the value of the integral `int_((-π)/4)^(π/4) "g"("f"(x))"d"x` is ______.
Let `int ((x^6 - 4)dx)/((x^6 + 2)^(1/4).x^4) = (ℓ(x^6 + 2)^m)/x^n + C`, then `n/(ℓm)` is equal to ______.
If f(x) = `{{:(x^2",", "where" 0 ≤ x < 1),(sqrt(x)",", "when" 1 ≤ x < 2):}`, then `int_0^2f(x)dx` equals ______.
Evaluate: `int_0^π 1/(5 + 4 cos x)dx`
Evaluate: `int_0^π x/(1 + sinx)dx`.
Evaluate `int_1^2(x+3)/(x(x+2)) dx`
Evaluate the following integral:
`int_0^1x (1 - x)^5 dx`
Evaluate the following integral:
`int_0^1 x(1-x)^5 dx`
