The area enclosed between the curves y=loge(x+e),x=loge(y1), and the x-axis is
The parabolas y2=4xandx2=4y divide the square region bounded by the lines x=4, y=4 and the coordinate axes. If S1,S2,S3 are the areas of these parts numbered from top to bottom, respectively, then
Let S be the area bounded by the curve y=sinx(0≤x≤π) and the x-axis and T be the area bounded by the curves y=sinx(0≤x≤2π),y=acosx(0≤x≤2π), and the x-axis (where a∈R+). The value of (3a) such that S:T=1:31 is___.
Two curves C1≡[f(y)]2/3+[f(x)]1/3=0andC2≡[f(y)]2/3+[f(x)]2/3=12, satisfying the relation (x−y)f(x+y)−(x+y)f(x−y)=4xy(x2−y2)
The area bounded by C1andC2 is
Let f:[0,∞)→R be a continuous function such that f(x)=1−2x+0∫xex−tf(t)dt for all x∈[0,∞). Then, which of the following statements(s) is (are)) TRUE?