Application of Integrals
In Figure, AOBA is the part of the ellipse 9x2+y2=36in the first quadrant such that OA=2andOB=6. Find the area between the arc AB and the chord AB.
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Find the area of the region bounded by the curve y2=xand the lines x=1,x=4and the x-axis.
Using integration find the area of the triangular region whose sides have the equations y=2x+1, y=3x+1 and x=4.
Find the area of the region bounded by the line y=3x+2, the x-axis and the ordinates x=1andx=1.
The area bounded by the y-axis, y=cosxand y=s∈xwhen 0≤x≤2πis(A) 2(2−1) (B) 2−1 (C) 2+1 (D) 2
Sketch and find the area bounded by the curve
If curve ∣x∣+∣y∣=a
divides the area in two parts, then find their ratio in the first quadrant only.
Using integration find the area of region bounded by the triangle whose vertices are (1,0),(1,3)and(3,2).
Using the method of integration find the area bounded by the curve ∣x∣+∣y∣=1.[Hint: The required region is bounded by lines x+y=1,x−y=1,−x+y=1and−x−y=1]˙
Sketch the graph of y=∣x+3∣and evaluate∫−60∣x+3∣dx.