Application of Integrals
The area of the region enclosed by the curves y=x,x=e,y=x1and the positive x-axis is
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Find the area enclosed by the parabola 4y=3x2 and the line 2y=3x+12
Find the area of the region lying in the first quadrant and bounded by y=4x2,x=0,y=1 and y=4.
Sketch the region common to the circle x2+y2=16 and the parabola x2=6y. Also, find the area of the region, using integration.
Using integration find the area of region bounded by the triangle whose vertices are (1, 0), (2, 2) and (3, 1).
Using integration, find the area of the region bounded by the line 2y=−x+8,x-axis is and the lines x=2 and x=4.
Prove that the curves y2=4xand x2=4ydivide the area of the square bounded by x=0,x=4,y=4andy=0into three equal parts.
The area of the circle x2+y2=16exterior to the parabola y2=6xis(A) 34(4π−3) (B) 34(4π+3)(C) 34(8π−3) (D) 34(8π+3)
Sketch the graph of y=∣x+3∣and evaluate∫−60∣x+3∣dx.