3.7.1 Integration Short Questions (Question 1)


Question 1:
Find the integral of each of the following . ( a ) ( 3 x 2 5 2 x 3 + 2 ) d x ( b ) x 2 ( x 5 + 2 x ) d x ( c ) 3 x 4 + 2 x x 3 d x ( d ) ( 7 + x ) ( 7 x ) x 4 d x ( e ) ( 5 x 1 ) 3 d x ( f ) 3 ( 4 x + 7 ) 8 d x


Solution:
(a)
( 3 x 2 5 2 x 3 + 2 ) d x = ( 3 x 2 5 x 3 2 + 2 ) d x = 3 x 1 + 5 x 2 4 + 2 x + c = 3 x + 5 4 x 2 + 2 x + c

(b)
x 2 ( x 5 + 2 x ) d x = ( x 7 + 2 x 3 ) d x = x 8 8 + 2 x 4 4 + c = x 8 8 + x 4 2 + c

(c)
3 x 4 + 2 x x 3 d x = ( 3 x 4 x 3 + 2 x x 3 ) d x = ( 3 x + 2 x 2 ) d x = 3 x 2 2 2 x + c

(d)
( 7 + x ) ( 7 x ) x 4 d x = ( 49 x 2 x 4 ) d x = ( 49 x 4 1 x 2 ) d x = ( 49 x 4 x 2 ) d x = 49 x 3 3 + 1 x + c = 49 3 x 3 + 1 x + c

(e)
( 5 x 1 ) 3 d x = ( 5 x 1 ) 4 ( 4 ) ( 5 ) + c = 1 20 ( 5 x 1 ) 4 + c

(f)
3 ( 4 x + 7 ) 8 d x = 3 ( 4 x + 7 ) 8 d x = 3 ( 4 x + 7 ) 7 ( 7 ) ( 4 ) + c = 3 28 ( 4 x + 7 ) 7 + c

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