Academia Aeternum
तमसो मा ज्योतिर्गमय
Wisdom · Knowledge · Eternity
Area Under Curves, Between Curves — Every Solution Fully Worked Out
3 exercise files · 39 total questions
\(A = \int_a^b y\,dx\ \text{(area under curve, above x-axis)}\)\(A = \int_a^b \big(f(x)-g(x)\big)\,dx\ \text{(between two curves)}\)\(\text{Circle }x^2+y^2=a^2:\ \text{Area (quadrant)} = \dfrac{\pi a^2}{4}\)\(\text{Always sketch the region before setting up limits}\)Step 1 — Sketch the curves and shade the required region before writing any integral. Step 2 — Find points of intersection algebraically to fix the limits of integration. Step 3 — Identify the upper and lower curve on the interval; set up A=∫(upper−lower)dx. Step 4 — If the region changes shape (upper/lower curve swaps) partway, split the integral at that x-value. Step 5 — Take the absolute value of area below the x-axis.
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