Advertisements
Advertisements
प्रश्न
Evaluate:
`int_0^1 |2x + 1|dx`
उत्तर
`int_0^1 |2x + 1|dx`
= `int_0^1 2x + 1 dx` ...`{{:("For" 0 < x < 1),(2x + 1 > 0),(∴ |2x + 1| = 2x + 1):}`
= `[2 x^2/2 + x]_0^1`
= `[x^2 + x]_0^1`
= (1 + 1) – (0 + 0)
= 2
APPEARS IN
संबंधित प्रश्न
By using the properties of the definite integral, evaluate the integral:
`int_0^(pi/2) sin^(3/2)x/(sin^(3/2)x + cos^(3/2) x) dx`
By using the properties of the definite integral, evaluate the integral:
`int_2^8 |x - 5| dx`
By using the properties of the definite integral, evaluate the integral:
`int_(pi/2)^(pi/2) sin^7 x dx`
Evaluate the definite integrals `int_0^pi (x tan x)/(sec x + tan x)dx`
`∫_4^9 1/sqrtxdx=`_____
(A) 1
(B) –2
(C) 2
(D) –1
\[\int\limits_0^a 3 x^2 dx = 8,\] find the value of a.
Using properties of definite integrals, evaluate
`int_0^(π/2) sqrt(sin x )/ (sqrtsin x + sqrtcos x)dx`
Evaluate the following integral:
`int_0^1 x(1 - x)^5 *dx`
`int_0^(pi/2) sqrt(cos theta) * sin^2 theta "d" theta` = ______.
`int_0^{pi/4} (sin2x)/(sin^4x + cos^4x)dx` = ____________
`int_-1^1x^2/(1+x^2) dx=` ______.
The value of `int_2^7 (sqrtx)/(sqrt(9 - x) + sqrtx)dx` is ______
Evaluate `int_0^(pi/2) (tan^7x)/(cot^7x + tan^7x) "d"x`
Show that `int_0^(pi/2) (sin^2x)/(sinx + cosx) = 1/sqrt(2) log (sqrt(2) + 1)`
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_0^(pi/2) "dx"/(("a"^2 cos^2x + "b"^2 sin^2 x)^2` (Hint: Divide Numerator and Denominator by cos4x)
`int (dx)/(e^x + e^(-x))` is equal to ______.
Evaluate: `int_0^(π/2) 1/(1 + (tanx)^(2/3)) dx`
Evaluate: `int_2^5 sqrt(x)/(sqrt(x) + sqrt(7) - x)dx`
`int_a^b f(x)dx = int_a^b f(x - a - b)dx`.
Let f be a real valued continuous function on [0, 1] and f(x) = `x + int_0^1 (x - t)f(t)dt`. Then, which of the following points (x, y) lies on the curve y = f(x)?
Let f be continuous periodic function with period 3, such that `int_0^3f(x)dx` = 1. Then the value of `int_-4^8f(2x)dx` is ______.
The value of the integral `int_0^1 x cot^-1(1 - x^2 + x^4)dx` is ______.
Evaluate: `int_1^3 sqrt(x + 5)/(sqrt(x + 5) + sqrt(9 - x))dx`
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_-2^3 1/(x + 5) dx`
Solve the following.
`int_0^1e^(x^2)x^3dx`