CAT Exam Model Paper 3 with solutions for free online practice

Question : 98 of 100

Marks: +1, -0

Find the area among y = 7 - x

^{2}

and the x-axis among the values x = - 1 and x = 2

Solution:

Given : limits a = − 1 and b = 2
Area under curve =

∫↙{a}↖{b}\f (x) \dx

Substitute the limits and f(x)

∫ ↙{{ - 1 }} ↖{ { 2 }} ( 7 - x ^ { 2 } ) d x

= ( 7 x - { x ^ { 3 } } /{ 3 } ) ^ { 2 }

= ( 7 ( 2 ) - { 2 ^ { 3 } } /{ 3 } ) - ( 7 ( - 1 ) - { ( - 1 ) ^ { 3 } }/ { 3 } )

= ( 14 - { 8 } /{ 3 } ) - ( - 7 + { 1 }/ { 3 } ) = { 34 } /{ 3 } + { 20 } /{ 3 } = 18 { \Units }

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