Application of Integrals
If A1,A2,A3,..are sets such that n(Ai)=101−i, A1⊃A2⊃A3⊃…⊃A100 and A=∩i=5100Ai then n(A) is equal to
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.
Area bounded by the curve y=x3, the x-axis and the ordinates x=2and x=1is(A) −9 (B) 4−15 (C) 415 (D) 417
The area bounded by the x-axis, the curve y=f(x), and the lines x=1,x=b is equal to b2+1−2 for all b>1, then f(x) is x−1 (b) x+1 x2+1 (d) 1+x2x