Title Chapter 8 Applications of Integrals.pdf ✅

(1) APPLICATION OF INTEGRALS 08 APPLICATION OF INTEGRALS 1. Elementary area: The area is called elementary area which is located at any arbitary position within the region which is specified by some value of x between a and b. 2. The 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 the formula: Area = ∫ vdx ௕ ௭ = ∫ f(x)dx ௕ ௭ 3. The area of the region bounded by the curve x = θ(y) , y-axis and the lines y = c, y = d is given by the formula: Area = ∫ xdy ௕ ௖ = ∫ θ(y)dy ௕ ௖ 4. The area of the region enclosed between two curves y = f (x), y = g (x) and the lines x = a, x = b is given by the formula, Area = ∫ [f(x) − g(x)]dx ௕ ௔ , where f(x) ≥ g(x) in [a, b]. 5. If f(x) ≥ g(x) in [a, c] and f(x) ≤ g(x) in [c, b], a < c < b, then we write the areas as: Area = න [f(x) − g(x)]dx + ௕ ௔ න [g(x) − f(x)]dx ௕ ௖
(2) APPLICATION OF INTEGRALS 08
(3) APPLICATION OF INTEGRALS 08 Important Questions Multiple Choice questions- 1. Area lying in the first quadrant and bounded by the circle x2 + y2 = 4 and the lines x = 0 and x = 2 is (a) π (b) గ ଶ (c) గ ଷ (d) గ ସ 2. Area of the region bounded by the curve y2 = 4x, y-axis and the line y = 3 is (a) 2 (b) ଽ ସ (c) ଽ ଷ (d) ଽ ଶ 3. Smaller area enclosed by the circle x2 + y2 = 4 and the line x + y = 2 is (a) 2 (π – 2) (b) π – 2 (c) 2π – 1 (d) 2 (π + 2). 4. Area lying between the curves y2 = 4x and y = 2 is: (a) ଶ ଷ (b) ଵ ଷ (c) ଵ ସ (d) ଷ ସ