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महाराष्ट्र राज्य शिक्षण मंडळएचएससी वाणिज्य (इंग्रजी माध्यम) इयत्ता १२ वी

∫1212x+3 dx = ______ - Mathematics and Statistics

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प्रश्न

`int_1^2 1/(2x + 3)  dx` = ______

रिकाम्या जागा भरा

उत्तर

`int_1^2 1/(2x + 3)  dx` = `bbunderline(1/2 log(7/5))`

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पाठ 1.6: Definite Integration - Q.2

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

\[\int_a^b xf\left( x \right)dx = \left( \frac{a + b}{2} \right) \int_a^b f\left( x \right)dx\]

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`


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