Application of Integrals
- Area of the region bounded by the curve y = f(x), x-axis, and the lines x = a and x = b (b > a) is given by
or
- The area of the region bounded by the curve x = g(y), y-axis, and the lines y = c and y = d is given by
or
- If a line y = mx + p intersects a curve y = f(x) at x = a and x = b, (b > a), then the area (A) of region bounded by the curve y = f(x) and the line y = mx + p is
- If a line y = mx + p intersects a curve x = g(y) at y = c and y = d ,(d > c), then the area (A) of region bounded by the curve x = g(y) and the line y = mx + p is
Example 1: Find the area of the region in the first and third quadrant enclosed by the x-axis and the line , and the ellipse
Solution: The given equations are
... (1)
... (2)
Substituting in equation (2), we obtain
Hence, the line meets the ellipse at C
and D
in the first and third quadrant respectively.
In the figure, CM ⊥ XX′
Now, area OCMO =
Area ACMA
- The area of the region enclosed bet…
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