08Class 12 Maths

Application of Integrals formulas

Area under curves using definite integrals. A rough sketch before you integrate prevents most of the errors in this chapter.

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Formulas

Area with the x-axis: $\displaystyle A = \int_a^b |y|\,dx$
Area with the y-axis: $\displaystyle A = \int_c^d |x|\,dy$
Between two curves: $\displaystyle A = \int_a^b [f(x) - g(x)]\,dx$
Where f(x) ≥ g(x).
Area of a circle: $\displaystyle \pi a^2$
For x² + y² = a². A useful check.
Area of an ellipse: $\displaystyle \pi ab$

Letting areas above and below the axis cancel. Split the integral where the curve crosses the axis.
Skipping the sketch, then using the wrong limits or the wrong curve on top.

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