Evaluate : `int 1/sqrt("x"^2 - 4"x" + 2) "dx"`

I = `int 1/sqrt("x"^2 - 4"x" + 2) "dx"` `= int "dx"/sqrt("x"^2 - 4"x" +4 - 2) ` `= int "dx"/sqrt(("x - 2")^2 -( sqrt 2)^2) "dx"` `= "log" |("x"-2) + sqrt(("x - 2")^2 -( sqrt 2)^2)| + "c"` `= "log" |("x"-2) + sqrt("x"^2 - 4"x" + 2)| + c`

Evaluate : Int 1/Sqrt(

प्रश्न

Evaluate : $\int \frac{1}{\sqrt{x^{2} - 4 x + 2}} dx$

बेरीज

उत्तर

I = $\int \frac{1}{\sqrt{x^{2} - 4 x + 2}} dx$

$= \int \frac{dx}{\sqrt{x^{2} - 4 x + 4 - 2}}$

$= \int \frac{dx}{\sqrt{{(x - 2)}^{2} - {(\sqrt{2})}^{2}}} dx$

$= log | (x - 2) + \sqrt{{(x - 2)}^{2} - {(\sqrt{2})}^{2}} | + c$

$= log | (x - 2) + \sqrt{x^{2} - 4 x + 2} | + c$

shaalaa.com

Properties of Definite Integrals

या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?

Q 1.H Q 1.G Q 2.A.i

2015-2016 (July)

APPEARS IN

2015-2016 (July) (with solutions)

Q 1.H | 2 marks

व्हिडिओ ट्यूटोरियलVIEW ALL [4]

view
व्हिडिओ ट्यूटोरियल For All Subjects
Properties of Definite Integrals

video tutorial00:07:37
Properties of Definite Integrals

video tutorial01:56:53
Properties of Definite Integrals

video tutorial00:26:24
Properties of Definite Integrals

video tutorial00:41:32

संबंधित प्रश्‍न

Evaluate : $\int e^{x} [\frac{\sqrt{1 - x^{2}} \sin^{- 1} x + 1}{\sqrt{1 - x^{2}}}] d x$

By using the properties of the definite integral, evaluate the integral:

$\int_{0}^{\frac{π}{4}} \log (1 + \tan x) d x$

By using the properties of the definite integral, evaluate the integral:

$\int_{0}^{\frac{π}{2}} \frac{\sin x - \cos x}{1 + \sin x \cos x} d x$

$\int_{4}^{9} \frac{1}{\sqrt{x}} d x =$ _____

(A) 1

(B) –2

(D) –1

Evaluate $\int e^{x} [\frac{\cos x - \sin x}{\sin^{2} x}] d x$

Evaluate : ∫ log (1 + x²) dx

$\int_{0}^{4} \frac{1}{1 + \sqrt{x}}$ dx = ______.

$\int_{- 9}^{9} \frac{x^{3}}{4 - x^{2}}$ dx = ______

$\int_{0}^{\frac{π}{2}} x \sin x d x$ = ______

$\int_{0}^{\frac{π}{4}} \frac{\sin 2 x}{\sin^{4} x + \cos^{4} x} d x$ = ____________

$\int_{\frac{π}{18}}^{\frac{4 π}{9}} \frac{2 \sqrt{\sin x}}{\sqrt{\sin x} + \sqrt{\cos x}}$ dx = ?

f(x) = ${\begin{cases} \frac{x^{3}}{k}; 0 \leq x \leq 2 \\ 0; otherwise \end{cases}$ is a p.d.f. of X. The value of k is ______

If $\int_{0}^{k} \frac{dx}{2 + 32 x^{2}} = \frac{π}{32},$ then the value of k is ______.

$\int_{0}^{π} \sin^{2} x . \cos^{2} x d x$ = ______

$\int_{- a}^{a} f (x) d x$ = 0 if f is an ______ function.

If $\int \frac{{(\log x)}^{2}}{x} dx = \frac{{(\log x)}^{k}}{k} + c$ , then the value of k is:

$\int \frac{d x}{e^{x} + e^{- x}}$ is equal to ______.

$\int_{- 5}^{5} \frac{x^{7}}{x^{4} + 10} d x$ = ______.

If $\int_{0}^{1} (\sqrt{2 x} - \sqrt{2 x - x^{2}}) d x = \int_{0}^{1} (1 - \sqrt{1 - y^{2}} - \frac{y^{2}}{2}) d y + \int_{1}^{2} (2 - \frac{y^{2}}{2}) d y$ + I then I equal.

If $\int_{- a}^{a} (| x | + | x - 2 |) d x$ = 22, (a > 2) and [x] denotes the greatest integer ≤ x, then $\int_{a}^{- a} (x + [x]) d x$ is equal to ______.

The integral $\int_{0}^{2} | | x - 1 | - x | d x$ is equal to ______.

$\int_{0}^{π} \frac{x \sin x}{1 + \cos^{2} x} d x$ equals ______.

Let f be continuous periodic function with period 3, such that $\int_{0}^{3} f (x) d x$ = 1. Then the value of $\int_{- 4}^{8} f (2 x) d x$ is ______.

Evaluate: $\int_{1}^{3} \frac{\sqrt{x + 5}}{\sqrt{x + 5} + \sqrt{9 - x}} d x$

$\int_{- 1}^{1} \frac{| x - 2 |}{x - 2} d x$ , x ≠ 2 is equal to ______.

Evaluate: $\int_{- π / 4}^{π / 4} \frac{\cos 2 x}{1 + \cos 2 x} d x$ .

Evaluate the following integral:

$\int_{0}^{1} x {(1 - 5)}^{5}$ dx

$\int_{0}^{2 a} \frac{f (x)}{f (x) + f (2 a - x)} d x$ = ______

Evaluate the following definite integral:

$\int_{1}^{3} \log x d x$

Evaluate the following definite integral:

$\int_{- 2}^{3} \frac{1}{x + 5} d x$

Solve the following.

$\int_{0}^{1} e^{x^{2}} x^{3} d x$

Evaluate the following integrals:

$\int_{- 9}^{9} \frac{x^{3}}{4 - x^{3}} d x$

Evaluate the following integral:

$\int_{- 9}^{9} \frac{x^{3}}{4 - x^{2}} d x$

Evaluate:

$\int_{0}^{6} | x + 3 | d x$

Evaluate the following definite intergral:

$\int_{1}^{2} \frac{3 x}{9 x^{2} - 1} d x$

Evaluate : Int 1/Sqrt("X"^2 - 4"X" + 2) "Dx" - Mathematics and Statistics

Advertisements

Advertisements

प्रश्न

उत्तर

APPEARS IN

व्हिडिओ ट्यूटोरियलVIEW ALL [4]

संबंधित प्रश्‍न

Select a course

Evaluate : Int 1/Sqrt("X"^2 - 4"X" + 2) "Dx" - Mathematics and Statistics

Advertisements

Advertisements

प्रश्न

उत्तरShow Solution

APPEARS IN

व्हिडिओ ट्यूटोरियलVIEW ALL [4]

संबंधित प्रश्‍न

Select a course

उत्तर