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

State whether the following statement is True or False: If ∫x f(x)dx=f(x)2, then f(x) = ex2 - Mathematics and Statistics

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प्रश्न

State whether the following statement is True or False:

If `int x  "f"(x) "d"x = ("f"(x))/2`, then f(x) = `"e"^(x^2)`

पर्याय

  • True

  • False

MCQ
चूक किंवा बरोबर

उत्तर

True

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  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1.5: Integration - Q.3

संबंधित प्रश्‍न

Integrate the functions:

`x/(9 - 4x^2)`


Integrate the functions:

`(sin x)/(1+ cos x)^2`


\[\int\sqrt{2 x^2 + 3x + 4} \text{ dx}\]

Write a value of\[\int\frac{\sec^2 x}{\left( 5 + \tan x \right)^4} dx\]


\[\int x \sin^3 x\ dx\]

Evaluate the following integrals : `int(4x + 3)/(2x + 1).dx`


Integrate the following functions w.r.t. x : `(1)/(x(x^3 - 1)`


Evaluate the following : `int (1)/sqrt(11 - 4x^2).dx`


Evaluate the following : `int (1)/(1 + x - x^2).dx`


Evaluate the following.

`int 1/(sqrt("x"^2 + 4"x"+ 29))` dx


State whether the following statement is True or False.

If `int x  "e"^(2x)` dx is equal to `"e"^(2x)` f(x) + c, where c is constant of integration, then f(x) is `(2x - 1)/2`.


Evaluate:

`int (5x^2 - 6x + 3)/(2x − 3)` dx


Evaluate: `int "x" * "e"^"2x"` dx


`int sqrt(1 + sin2x)  "d"x`


`int(log(logx))/x  "d"x`


`int dx/(2 + cos x)` = ______.

(where C is a constant of integration)


`int(1 - x)^(-2)` dx = `(1 - x)^(-1) + c`


`int secx/(secx - tanx)dx` equals ______.


Evaluate the following.

`int x^3/(sqrt(1+x^4))dx`


If f′(x) = 4x3 − 3x2 + 2x + k, f(0) = -1 and f(1) = 4, find f(x)


If f ′(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x)


Evaluate the following.

`int x sqrt(1 + x^2)  dx`


Evaluate:

`int 1/(1 + cosα . cosx)dx`


Evaluate.

`int (5x^2 - 6x + 3)/(2x - 3) dx`


Evaluate:

`int sqrt((a - x)/x) dx`


Evaluate the following.

`intx sqrt(1 +x^2)  dx`


Evaluate the following.

`int1/(x^2+4x-5)dx`


If f'(x) = 4x3 – 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).


Evaluate:

`intsqrt(sec  x/2 - 1)dx`


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