Question

calculate area uder curve for shaded region...

Correct answers only or else report and 0 star rate​

Answer 1

AnswEr :

Geometrical Significance of Integration

Summation of infinitesimally small units under the curve to find the area covered by the curve.

We have to calculate the area under the curve y = x².

Integrating the above function w.r.t x,

$\displaystyle \sf \: y = \int {x}^{2} dx \\ \\ \implies \sf \: y = \dfrac{x {}^{2 + 1} }{2 + 1} \\ \\ \implies \sf \: y = \dfrac{ \: \: x {}^{3} }{3}$

Here, the upper limit is 2 and low limit is 0.

Substituting the limits in the above expression,

$\implies \sf \: y = \dfrac{ \: \: {2}^{3} }{3} - \dfrac{ \: {0}^{3} }{3} \\ \\ \implies \boxed{ \boxed{ \sf y = \dfrac{8}{3} \: sq. units}}$