Advertisements
Advertisements
प्रश्न
If `int_0^alpha(3x^2+2x+1)dx=14` then `alpha=`
(A) 1
(B) 2
(C) –1
(D) –2
उत्तर
(B) 2
`int_0^alpha (3x^2+2x+1)dx=14`
`[x^3+x^2+x]_0^alpha=14`
`alpha^3+alpha^2+alpha-14=0`
`(alpha-2)(alpha^2+3alpha+7)=0`
But `alpha^2+3alpha+7=0` does not have real roots
`alpha=2`
APPEARS IN
संबंधित प्रश्न
If `int_0^alpha3x^2dx=8` then the value of α is :
(a) 0
(b) -2
(c) 2
(d) ±2
Evaluate : `intlogx/(1+logx)^2dx`
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^(pi/4) log (1+ tan x) dx`
By using the properties of the definite integral, evaluate the integral:
`int_0^(2x) cos^5 xdx`
By using the properties of the definite integral, evaluate the integral:
`int_0^(pi/2) (sin x - cos x)/(1+sinx cos x) dx`
By using the properties of the definite integral, evaluate the integral:
`int_0^a sqrtx/(sqrtx + sqrt(a-x)) dx`
The value of `int_0^(pi/2) log ((4+ 3sinx)/(4+3cosx))` dx is ______.
Evaluate : `int _0^(pi/2) "sin"^ 2 "x" "dx"`
Evaluate : ∫ log (1 + x2) dx
Evaluate `int_1^3 x^2*log x "d"x`
The c.d.f, F(x) associated with p.d.f. f(x) = 3(1- 2x2). If 0 < x < 1 is k`(x - (2x^3)/"k")`, then value of k is ______.
`int_0^(pi"/"4)` log(1 + tanθ) dθ = ______
The value of `int_-3^3 ("a"x^5 + "b"x^3 + "c"x + "k")"dx"`, where a, b, c, k are constants, depends only on ______.
`int_0^4 1/(1 + sqrtx)`dx = ______.
`int_"a"^"b" sqrtx/(sqrtx + sqrt("a" + "b" - x)) "dx"` = ______.
`int_0^1 (1 - x)^5`dx = ______.
`int_{pi/6}^{pi/3} sin^2x dx` = ______
`int_0^{1/sqrt2} (sin^-1x)/(1 - x^2)^{3/2} dx` = ______
If `int_0^"k" "dx"/(2 + 32x^2) = pi/32,` then the value of k is ______.
`int_(-pi/4)^(pi/4) 1/(1 - sinx) "d"x` = ______.
`int_0^1 "e"^(5logx) "d"x` = ______.
Find `int_2^8 sqrt(10 - x)/(sqrt(x) + sqrt(10 - x)) "d"x`
`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:
The value of `int_0^1 tan^-1 ((2x - 1)/(1 + x - x^2)) dx` is
Evaluate: `int_0^(π/2) 1/(1 + (tanx)^(2/3)) dx`
If `int_a^b x^3 dx` = 0, then `(x^4/square)_a^b` = 0
⇒ `1/4 (square - square)` = 0
⇒ b4 – `square` = 0
⇒ (b2 – a2)(`square` + `square`) = 0
⇒ b2 – `square` = 0 as a2 + b2 ≠ 0
⇒ b = ± `square`
`int_4^9 1/sqrt(x)dx` = ______.
If `intxf(x)dx = (f(x))/2` then f(x) = ex.
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 ______.
What is `int_0^(π/2)` sin 2x ℓ n (cot x) dx equal to ?
`int_-1^1 |x - 2|/(x - 2) dx`, x ≠ 2 is equal to ______.
Evaluate : `int_-1^1 log ((2 - x)/(2 + x))dx`.
Evaluate the following definite integral:
`int_4^9 1/sqrt"x" "dx"`
Evaluate `int_0^3root3(x+4)/(root3(x+4)+root3(7-x)) dx`
`int_-9^9 x^3/(4-x^2) dx` =______
Evaluate the following definite integral:
`int_1^3 log x dx`
Evaluate the following integral:
`int_0^1 x (1 - x)^5 dx`
