How do you evaluate the definite integral $int1/(x^2sqrtx)$ from $[1,4]$ ?

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Answer 1 · 2016-08-21T11:47:31

$7/12$

$int_a^b$ $1/(x^2.sqrt2)$ must be written as an integral of a power of x

$sqrt2$ = $x^(1/2)$
So the denominator is $x ^(5/2)$

So the function can be written as $x^(-5/2)$

$int_1^4$ $x^(-5/2)$ .dx = [ $-2/3x^(-3/2)$ ] from 4 to 1

When $x$ =4 $x^(-3/2)$ = $1/8$

$-2/3$ x $1/8$ = $-1/12$

When $x$ =1 $x^(-3/2)$ =1

$-2/3$ x 1= $-2/3$

$-1/12$ -( $-2/3$ )= $7/12$

How do you evaluate the definite integral int1/(x^2sqrtx)int1/(x^2sqrtx) from [1,4][1,4]?