The length of curve: `y=f(x)` between `x=a` and `x=b` is given by

Given the curve y=f(x)

The area under the curve f(x) bounded by x=a and x=b is given by

The area bounded by the curve y=f(x) ,above the x-axis, between x=a and x=b is modulus of:

The area bounded by the x-axis the curve y = f(x) and the lines x = a and x = b is equal to sqrt(b^(2) - a^(2)) AA b > a (a is constant). Find one such f(x).

In the adjacent figure the graph of two function y=f(x) and y=sin x are given y=sin x intersects, y=f(x) at A(a,f(a)), B(pi,0) and C(2pi,0) . A_(i)(i=1,2,3) is the area bounded by the curves y=f(x) and y=sin x between x=0 and x=a,i=1 between x=a and x=pi, i=2 between x=pi and x=2pi,i=3 . If A_(1)=1-sin a+(a-1) cos a, determine the function f(x). Hence, determine a and A_(1) . Also, calculate A_(2) and A_(3) . .

If A is the area lying between the curve y=sin x and x-axis between x=0 and x=pi//2 . Area of the region between the curve y=sin 2x and x -axis in the same interval is given by

Statement 1: The area bounded by parabola y=x^(2)-4x+3 and y=0 is (4)/(3) sq.units. Statement 2: The area bounded by curve y=f(x)>=0 and y=0 between ordinates x=a and x=b (where b>a) is int_(a)^(b)f(x)dx

Compute the arc length of the curve y= ln cos x between the points with the abscissas x=0, x= (pi)/(4)