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The area bounded by the curve f(x) = x + sin x and its inverse function between the ordinates x= 0 to x = , is
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Correct option is D
Clearly,f:[0,2π]→[0,2π] given byf(x) =x + sin x is a bijection. So, its inverse exists, the graph of f−1(x) is the mirror image of the graph of f(x) in the line y = x.∴ Required area = 4 (Area of one loop) =4∫0π (x+sinx)dx−∫0π xdx=4∫0π sinxdx=−4[cosx]0π=−4[cosπ−cos0]=8 sq unitsTalk to our academic expert!
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Let f(x) be a non-negative continuous function such that the area bounded by the curve y =f(x), X-axis and the ordinates is then, is equal to
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