Application of Integrals
Find the area of the region bounded by the curves y2=2y−x and the y-axis.
The area bounded by the two branches of curve (y−x)2=x3 and the straight line x=1 is 51squ˙nits (b) 53squ˙nits 54squ˙nits (d) 48squ˙nits
Draw a rough sketch of the curve y=x2−3x+2x2+3x+2 and find the area of the bounded region between the curve and the x-axis.
Sketch the region common to the circle x2+y2=16 and the parabola x2=6y. Also, find the area of the region, using integration.
Sketch and find the area bounded by the curve ∣x∣+∣y∣=aandx2+y2=a2(wherea>0) If curve ∣x∣+∣y∣=a divides the area in two parts, then find their ratio in the first quadrant only.
The area of the region whose boundaries are defined by the curves y=2cosx,y=3tanx,andthey−aξsis 1+31n(32)squ˙nits 1+231n3−31n2squ˙nits 1+231n3−1n2squ˙nits 1n3−1n2squ˙nits
Let C be a curve passing through M(2,2) such that the slope of the tangent at anypoint to the curve is reciprocal of the ordinate of the point. If the area bounded by curve C and lin x=2i s A ,t h e nt h e v a l u e of 23Ai s__