Ch 8 applies definite integrals to find areas of regions bounded by curves, lines, and axes. Students calculate areas under curves, between two curves, and bounded by standard conics.
Area between y = f(x), x-axis, x = a, and x = b: A = ∫ₐᵇ f(x) dx (when f(x) ≥ 0). If curve is below x-axis, take |∫|. For area w.r.t. y-axis: A = ∫ₐᵇ g(y) dy.
Area between y = f(x) and y = g(x) from a to b: A = ∫ₐᵇ |f(x) − g(x)| dx. Find intersection points first to determine limits.
Download: https://ncert.nic.in/textbook/pdf/lemh202.pdf | Complete book Part II: https://ncert.nic.in/textbook/pdf/lemh2ps.zip
When f(x) < 0, the integral ∫f(x)dx is negative. Since area is always positive, take the absolute value: A = |∫ₐᵇ f(x) dx|. Or split the integral at points where the curve crosses the x-axis.
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