Find the area bounded by the curve y = sin x between x = 0 and x = 2 . - Wired Faculty

Vector Algebra

Question

Find the area bounded by the curve y = sin x between x = 0 and x = 2 $straight pi$ .

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Solution

The equation of curve is y = sin x. Its rough sketch from x = 0 to x - 2

straight pi

is shown is the figure.

Required area =

integral subscript 0 superscript straight pi space sinx space dx space plus space integral subscript straight pi superscript 2 straight pi end superscript left parenthesis negative sin space straight x right parenthesis space dx

open curly brackets because space sin space straight x space greater or equal than 0 space for space straight x space element of space left square bracket 0 comma space straight pi right square bracket space and space sin space straight x space less or equal than space 0 space for space straight x space element of space left square bracket straight pi comma space 2 straight pi close curly brackets

equals space left square bracket negative cos space straight x right square bracket subscript 0 superscript straight pi plus open square brackets cos space straight x close square brackets subscript straight pi superscript 2 straight pi end superscript space equals space left parenthesis negative cos space straight pi space plus space cos space 0 right parenthesis space plus space left parenthesis cos space 2 straight pi space minus space cos space straight pi right parenthesis equals space left parenthesis 1 plus 1 right parenthesis plus left parenthesis 1 plus 1 right parenthesis space equals space 4 space sq. space units.

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