Advertisements
Advertisements
प्रश्न
Evaluate: `int_(-π//4)^(π//4) (cos 2x)/(1 + cos 2x)dx`.
Advertisements
उत्तर
`int_(-π//4)^(π//4) (cos 2x)/(1 + cos 2x)dx = int_(-π//4)^(π//4) (2 cos^2 x - 1)/(2 cos^2 x)dx`
= `1/2 . 2 int_0^(π//4) (2 - sec^2 x)dx` ...[even function]
= `1/2 . 2[2x - tan x]_0^(π//4)`
= `π/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 : `intsec^nxtanxdx`
If `int_0^alpha(3x^2+2x+1)dx=14` then `alpha=`
(A) 1
(B) 2
(C) –1
(D) –2
By using the properties of the definite integral, evaluate the integral:
`int_0^1 x(1-x)^n dx`
By using the properties of the definite integral, evaluate the integral:
`int_0^2 xsqrt(2 -x)dx`
`int_(-pi/2)^(pi/2) (x^3 + x cos x + tan^5 x + 1) dx ` is ______.
Evaluate: `int_1^4 {|x -1|+|x - 2|+|x - 4|}dx`
Evaluate : \[\int(3x - 2) \sqrt{x^2 + x + 1}dx\] .
Prove that `int _a^b f(x) dx = int_a^b f (a + b -x ) dx` and hence evaluate `int_(pi/6)^(pi/3) (dx)/(1 + sqrt(tan x))` .
Evaluate : `int 1/sqrt("x"^2 - 4"x" + 2) "dx"`
The total revenue R = 720 - 3x2 where x is number of items sold. Find x for which total revenue R is increasing.
Prove that `int_0^"a" "f" ("x") "dx" = int_0^"a" "f" ("a" - "x") "d x",` hence evaluate `int_0^pi ("x" sin "x")/(1 + cos^2 "x") "dx"`
`int_2^7 sqrt(x)/(sqrt(x) + sqrt(9 - x)) dx` = ______.
`int_-9^9 x^3/(4 - x^2)` 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 log(1/x - 1) "dx"` = ______.
`int_-1^1x^2/(1+x^2) dx=` ______.
`int_0^9 1/(1 + sqrtx)` dx = ______
Which of the following is true?
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 = ______.
If `f(a + b - x) = f(x)`, then `int_0^b x f(x) dx` is equal to
`int_((-π)/2)^(π/2) log((2 - sinx)/(2 + sinx))` is equal to ______.
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 `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`
Solve the following.
`int_0^1e^(x^2)x^3dx`
Evaluate the following definite integral:
`int_-2^3(1)/(x + 5) dx`
\[\int_{-2}^{2}\left|x^{2}-x-2\right|\mathrm{d}x=\]
