Please help with the solution step by step

Asked by NITISH DAS | 15th Apr, 2020, 12:13: AM

Expert Answer:

The sketch of f(x) is shown below, with regions bounded by f(x) and the x-axis indicated by P, Q and R.
integral subscript a superscript d f left parenthesis x right parenthesis d x equals negative 7 comma space integral subscript b superscript d f left parenthesis x right parenthesis d x equals negative 2 space a n d space integral subscript c superscript a f left parenthesis x right parenthesis d x equals 17 comma space w h a t space i s space t h e space v a l u e space o f space integral subscript b superscript c f left parenthesis x right parenthesis d x ?
S o l u t i o n colon negative
integral subscript a superscript d f left parenthesis x right parenthesis d x equals negative 7
rightwards double arrow integral subscript a superscript b f left parenthesis x right parenthesis d x space plus thin space integral subscript b superscript c f left parenthesis x right parenthesis d x space plus space integral subscript c superscript d f left parenthesis x right parenthesis d x space equals space minus 7
S i n c e comma space space integral subscript b superscript d f left parenthesis x right parenthesis d x equals negative 2
rightwards double arrow integral subscript a superscript b f left parenthesis x right parenthesis d x space minus space 2 space equals space minus 7
rightwards double arrow integral subscript a superscript b f left parenthesis x right parenthesis d x equals negative 5 space... space left parenthesis i right parenthesis
G i v e n colon space integral subscript c superscript a f left parenthesis x right parenthesis d x equals 17 space space rightwards double arrow integral subscript a superscript c f left parenthesis x right parenthesis d x equals negative 17
rightwards double arrow integral subscript a superscript b f left parenthesis x right parenthesis d x space plus thin space integral subscript b superscript c f left parenthesis x right parenthesis d x equals negative 17
F r o m space left parenthesis i right parenthesis comma
rightwards double arrow negative 5 plus thin space integral subscript b superscript c f left parenthesis x right parenthesis d x equals negative 17
rightwards double arrow integral subscript b superscript c f left parenthesis x right parenthesis d x equals negative 12

Answered by Renu Varma | 15th Apr, 2020, 11:04: AM