A curve is given parametrically by x=1-t^ 2

MATHEMATICS · Multi-part · CBSE · Mathematics · Applications of Integrals · Applications of Integrals

Problem

A curve

C

is given parametrically by

x=1-t^{2}, \quad y=2t, \quad -1\le t\le 2.

Let

T

be the region bounded by the curve

C

and the

y

-axis. (a) Eliminate the parameter

t

to express

x

explicitly as a function of

y

. (b) Determine the

y

-values corresponding to the endpoints of the parameter interval

-1\le t\le 2

. (c) Write a single definite integral with respect to

y

that represents the area of

T

. Do not evaluate at this stage. (d) Evaluate the integral from part (c) to obtain the exact area of

T