Advertisements
Advertisements
प्रश्न
Integrate the function `1/sqrt(8+3x - x^2)`
Advertisements
उत्तर
Let `I = int 1/sqrt(8 + 3x - x^2) dx`
`= int dx/sqrt(8 - (x^2 - 3x))`
`= int dx/sqrt(8 - (x^2 - 2 * 3/2 x + 9/4) + 9/4)`
`= int dx/sqrt(41/4 - (x - 3/2)^2)`
`= int dx/sqrt((sqrt41/2)^2 - (x - 3/2)^2)` `...[∵ int dx/sqrt (a^2 - x^2) = sin^-1 x/a + C]`
`= sin^-1 ((x - 3/2)/(sqrt41/2)) + C`
`= sin^-1 ((2x - 3)/sqrt41) + C`
APPEARS IN
संबंधित प्रश्न
Find:
`int(x^3-1)/(x^3+x)dx`
Evaluate:
`int((x+3)e^x)/((x+5)^3)dx`
Integrate the function `(3x)/(1+ 2x^4)`
Integrate the function `1/sqrt((x - a)(x - b))`
Integrate the function `(5x - 2)/(1 + 2x + 3x^2)`
Integrate the function `(6x + 7)/sqrt((x - 5)(x - 4))`
Integrate the function `(x+2)/sqrt(x^2 + 2x + 3)`
`int dx/(x^2 + 2x + 2)` equals:
Integrate the function:
`sqrt(1- 4x^2)`
Integrate the function:
`sqrt(x^2 + 4x + 6)`
Integrate the function:
`sqrt(1-4x - x^2)`
Integrate the function:
`sqrt(x^2 + 3x)`
\[\int\frac{8x + 13}{\sqrt{4x + 7}} \text{ dx }\]
\[\int\frac{1 + x + x^2}{x^2 \left( 1 + x \right)} \text{ dx}\]
Find : \[\int\left( 2x + 5 \right)\sqrt{10 - 4x - 3 x^2}dx\] .
Find:
`int_(-pi/4)^0 (1+tan"x")/(1-tan"x") "dx"`
Find: `int (dx)/(x^2 - 6x + 13)`
What is a standard integral?
Evaluate \[\int \frac{dx}{a^2-x^2}\].
Evaluate \[\int \frac{dx}{\sqrt{x^2-a^2}}\].
Evaluate \[\int \frac{dx}{\sqrt{x^2+a^2}}\].
Which trigonometric substitution is suitable for \[a^2-x^2\] and \[\sqrt{a^2-x^2}\]?
Which method transforms \[\int\frac{dx}{ax^2+bx+c}\] or \[\int\frac{dx}{\sqrt{ax^2+bx+c}}\] into an expression compatible with standard formulae?
Which expression is the general transformation obtained by completing the square?
For \[\int\frac{px+q}{ax^2+bx+c}\,dx\], how is \[px+q\] written in relation to the derivative of the denominator?
What is the completed-square form of \[3x^2+13x-10\]?
For \[x+2=A(4x+6)+B\], what are the values of \[A\] and \[B\]?
