Advertisements
Advertisements
प्रश्न
`int_1^2 1/(2x + 3) dx` = ______
उत्तर
`int_1^2 1/(2x + 3) dx` = `bbunderline(1/2 log(7/5))`
APPEARS IN
संबंधित प्रश्न
Prove that: `int_0^(2a)f(x)dx=int_0^af(x)dx+int_0^af(2a-x)dx`
If `int_0^alpha(3x^2+2x+1)dx=14` then `alpha=`
(A) 1
(B) 2
(C) –1
(D) –2
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
Evaluate `int_0^(pi/2) cos^2x/(1+ sinx cosx) dx`
If \[f\left( a + b - x \right) = f\left( x \right)\] , then prove that
Evaluate : \[\int(3x - 2) \sqrt{x^2 + x + 1}dx\] .
Evaluate : `int 1/("x" [("log x")^2 + 4]) "dx"`
Find : `int_ (2"x"+1)/(("x"^2+1)("x"^2+4))d"x"`.
Evaluate the following integrals : `int_2^5 sqrt(x)/(sqrt(x) + sqrt(7 - x))*dx`
`int_0^1 ((x^2 - 2)/(x^2 + 1))`dx = ?
`int_0^1 (1 - x/(1!) + x^2/(2!) - x^3/(3!) + ... "upto" ∞)` e2x 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^{pi/2}((3sqrtsecx)/(3sqrtsecx + 3sqrt(cosecx)))dx` = ______
`int_0^(pi/2) sqrt(cos theta) * sin^2 theta "d" theta` = ______.
f(x) = `{:{(x^3/k; 0 ≤ x ≤ 2), (0; "otherwise"):}` is a p.d.f. of X. The value of k is ______
The value of `int_1^3 dx/(x(1 + x^2))` is ______
`int_(pi/4)^(pi/2) sqrt(1-sin 2x) dx =` ______.
`int_0^(pi/2) 1/(1 + cos^3x) "d"x` = ______.
`int_0^1 "e"^(5logx) "d"x` = ______.
`int_(-1)^1 (x + x^3)/(9 - x^2) "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 ______.
`int_(-2)^2 |x cos pix| "d"x` is equal to ______.
`int_(-"a")^"a" "f"(x) "d"x` = 0 if f is an ______ function.
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)
If `f(a + b - x) = f(x)`, then `int_0^b x f(x) dx` is equal to
`int_(-5)^5 x^7/(x^4 + 10) dx` = ______.
Evaluate: `int_0^(π/2) 1/(1 + (tanx)^(2/3)) dx`
Evaluate: `int_(-1)^3 |x^3 - x|dx`
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//4) log (1 + tanx)dx`.
If `int_0^(2π) cos^2 x dx = k int_0^(π/2) cos^2 x dx`, then the value of k is ______.
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_4^9 1/sqrt"x" "dx"`
Evaluate `int_1^2(x+3)/(x(x+2)) dx`
Evaluate the following integral:
`int_0^1 x(1 - x)^5 dx`
Solve the following.
`int_2^3x/((x+2)(x+3))dx`
Solve.
`int_0^1e^(x^2)x^3dx`