Integral Calculus

Evaluate the double integral of \(r \sin u dr du\), the limits of r is 0 and \(\cos u\) and the limits of u are 0 and pi.

Evaluate the integral of \((3x^2+9y^2) dx dy\) if the interior limits has an upper limit of y and a lower limit of 0, and whose outer limit has an upper limit of 2 and lower limit of 0.

Evaluate \(\int_0^{\pi/2}\int_0^1\int_0^2 z dz r^2 dr \sin u du\).

Find the area of the region bounded by \(y^2=8x\) and \(y=2x\).

What is the area bounded by the curve \(x^2=-9y\) and the line \(y+1=0\)?

What is the area (in square units) bounded by the curve \(y^2=x\) and the line \(x-4=0\)?

Find the area bounded by the curve \(y=x^2+2\), and the lines \(x=0\) and \(y=0\) and \(x=4\).

Find the area bounded by the parabolas \(y=6x-x^2\) and \(y=x^2-2x\). Note: The parabolas intersect at points \((0,0)\) and \((4,8)\).

Find the area bounded by the parabola \(x^2=4y\) and \(y=4\).

Find the area bounded by the line \(x-2y+10=0\), the x-axis, the y-axis and \(x=10\).

What is the area (in square units) bounded by the curve \(y^2=4x\) and \(x^2=4y\)?

Find the area enclosed by the curve \(x^2+8y+16=0\) the x-axis, the y-axis and the line \(x-4=0\).

What is the area bounded by the curve \(y=x^3\), the x-axis and the line \(x=-2\) and \(x = 1\)?

Find the area in the first quadrant bounded by the parabola \(y^2=4x\), \(x=1\) & \(x=3\)

Find the area (in sq. units) bounded by the parabolas \(x^2-2y=0\) and \(x^2+2y-8=0\).

What is the area between \(y=0\), \(y=3x^2\) \(x=0\) and \(x=2\)?

What is the area bounded by the curve \(y^2=x\) and the line \(x-4=0\)?

Find the area of the curve \(r^2=a^2 \cos 2\theta\).

Locate the centroid of the plane area bounded by \(y=x^2\) and \(y=x\).

Find the coordinates of the centroid of the plane area bounded by the parabola \(y=4-x^2\) and the x-axis.