Advertisements
Advertisements
प्रश्न
If `int_0^1 "e"^"t"/(1 + "t") "dt"` = a, then `int_0^1 "e"^"t"/(1 + "t")^2 "dt"` is equal to ______.
विकल्प
`"a" - 1 + "e"/2`
`"a" + 1 - "e"/2`
`"a" - 1 - "e"/2`
`"a" + 1 + "e"/2`
Advertisements
उत्तर
If `int_0^1 "e"^"t"/(1 + "t") "dt"` = a, then `int_0^1 "e"^"t"/(1 + "t")^2 "dt"` is equal to `"a" + 1 - "e"/2`.
Explanation:
Since I = `int_0^1 "e"^"t"/(1 + "t") "dt"`
= `|1/(1 + "t") "e"^"t"|_0^1 + int_0^1 "e"^"t"/(1 + "t")^2 "dt"` = a ...(Given)
Therefore, `int_0^1 "e"^"t"/(1 + "t")^2 = "a" - "e"/2 + 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
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/2) (2log sin x - log sin 2x)dx`
By using the properties of the definite integral, evaluate the integral:
`int_0^pi (x dx)/(1+ sin x)`
By using the properties of the definite integral, evaluate the integral:
`int_0^4 |x - 1| dx`
`int_(-pi/2)^(pi/2) (x^3 + x cos x + tan^5 x + 1) dx ` is ______.
`∫_4^9 1/sqrtxdx=`_____
(A) 1
(B) –2
(C) 2
(D) –1
`int_2^7 sqrt(x)/(sqrt(x) + sqrt(9 - x)) dx` = ______.
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_0^(pi/2) sqrt(cos theta) * sin^2 theta "d" theta` = ______.
`int_0^{pi/4} (sin2x)/(sin^4x + cos^4x)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^{pi/2} cos^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_-1^1x^2/(1+x^2) dx=` ______.
`int_0^(pi/2) 1/(1 + cosx) "d"x` = ______.
`int_(-1)^1 (x + x^3)/(9 - x^2) "d"x` = ______.
`int_0^(2"a") "f"(x) "d"x = 2int_0^"a" "f"(x) "d"x`, if f(2a – x) = ______.
Evaluate the following:
`int_(-pi/4)^(pi/4) log|sinx + cosx|"d"x`
If `int_0^"a" 1/(1 + 4x^2) "d"x = pi/8`, then a = ______.
`int_(-5)^5 x^7/(x^4 + 10) 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`
If `int_0^1(sqrt(2x) - sqrt(2x - x^2))dx = int_0^1(1 - sqrt(1 - y^2) - y^2/2)dy + int_1^2(2 - y^2/2)dy` + I then I equal.
`int_0^π(xsinx)/(1 + cos^2x)dx` equals ______.
`int_((-π)/2)^(π/2) log((2 - sinx)/(2 + sinx))` is equal to ______.
`int_-1^1 (17x^5 - x^4 + 29x^3 - 31x + 1)/(x^2 + 1) dx` is equal to ______.
If `int_0^(2π) cos^2 x dx = k int_0^(π/2) cos^2 x dx`, then the value of k is ______.
`int_0^(2a)f(x)/(f(x)+f(2a-x)) dx` = ______
Solve the following.
`int_0^1 e^(x^2) x^3dx`
Evaluate:
`int_0^sqrt(2)[x^2]dx`
What is the value of a definite integral when its upper and lower limits are equal?
Which property is useful for piecewise functions or modulus (absolute value) functions?
Which expression is equal to \[\frac{1}{1+\sqrt{\tan x}}\] in the evaluation of \[\int_{\frac{\pi}{6}}^{\frac{\pi}{3}}\frac{dx}{1+\sqrt{\tan x}}\]?
