Question

integrate xsqrt(4-x) dx by using integration by parts method.

Answer 1

\[\int x \times \sqrt{4-x} dx = x \int \sqrt{4-x} dx - \int [ \int \sqrt{4-x}dx \times \frac{dx}{dx}]\]

Answer 2

\[x \times \frac{2}{3} (4 -x)^{\frac{3}{2}} - \frac{2}{3} \times \frac{2}{5} \times (4-x)^{\frac{5}{2}}\]

Answer 3

the answers is \[2/3 (4-x)^{5/2} - 8/3 (4-x)^{3/2} +c\]

Answer 4

okay I am back let me do this again

Answer 5

ah you do remember the formula don't you

Answer 6

yeah i do i tried the question with v = (4-x)^1/2 and u = x

Answer 7

it gets me the wrong answer

Answer 8

i used u substitution by letting u= 4-x and i get the right answer but its not using the method that i want to lol

Answer 9

\[x \int \sqrt{4-x} dx - \int[ \int\sqrt{4-x}dx \times \frac{dx}{dx}]\]

Answer 10

ill brb :)

Answer 11

\[-x \times \frac{(4-x)^{1 + \frac{1}{2}}}{1 + \frac{1}{2}} - \int \frac{(4-x)^{1 + \frac{1}{2}}}{1 + \frac{1}{2}}dx\]

Answer 12

\[-x \times \frac{(4-x)^{\frac{3}{2}}}{\frac{3}{2}} - \frac{1}{\frac{3}{2}} \times \frac{(4-x)^{\frac{3}{2} + 1 }}{ 1 + \frac{3}{2}} \]

Answer 13

\[ -x \times \frac{2}{3} \times (4-x)^{\frac{3}{2}} - \frac{2}{3} \times \frac{2}{5} \times (4-x)^{\frac{5}{2}}\]

Answer 14

ah I did that again I am still getting the same with a sign reverse

Answer 15

ah Let's try this again with different approach

Answer 16

\[4- x = t \]
\[-dx = dt\]

Answer 17

\[x = 4-t\]

Answer 18

\[\int ( 4- t )(-1)(\sqrt t) dt\]

Answer 19

\[\int (t - 4 ) \sqrt t dt \]

Answer 20

\[ \int t^{1 + \frac{1}{2}} - 4 \times t^{\frac{1}{2}}\]

Answer 21

\[\int t^{1 + \frac{1}{2}} - 4 \times t^{\frac{1}{2}}dt\]

Answer 22

\[\int t^{\frac{3}{2}}dt - 4 \int t^{\frac{1}{2}}dt\]

Answer 23

\[ \frac{t^{\frac{3}{2} +1 }}{\frac{3}{2} +1 } - 4 \frac{t^{\frac{1}{2} +1 }}{\frac{1}{2}+1}\]

Answer 24

\[\frac{2}{5} \times t^{\frac{5}{2}} - 4 \times \frac{2}{3} \times t^{\frac{3}{2}}\]

Answer 25

\[\frac{2}{5} \times (4-x)^{\frac{5}{2}} - \frac{8}{3} \times (4-x)^{\frac{3}{2}}\]

Answer 26

ah I am sure this is correct