The area of the closed figure bounded by x=−1,y=0,y=x2+x+1, and the tangent to the curve y=x2+x+1 at A(1,3) is
If a(a>0) is the value of parameter for each of which the are of the figure bounded by the straight line y=1+a4a2−ax and the parabola y=1+a4x2+2ax+3a2 is the greatest, then the value of a4 is ___
If the area bounded by the x-axis, the curve y=f(x),(f(x)>0) and the lines x=1,x=b is equal to b2+1−2 for all b>1, then find f(x).
Consider the two curves C1:y=1+cosxandC2:y=1+cos(x−α) for α∈(0,2π), where x∈[0,π]. Also the area of the figure bounded by the curves C1,C2,andx=0 is same as that of the figure bounded by C2,y=1,andx=π.
For the values of α, the area bounded by C1,C2,x=0andx=π is