Find the area bounded by y = 4x + 3 with x- axis between the lines x = 1 and x = 4

Sketch the graph \(y=\left| x+3 \right| \) and evaluate \(\int _{ -6 }^{ 0 }{ \left| x+3 \right| } \) dx.

Using integration find the area of the region bounded between the line x = 4 and the parabola y² = 16x.

Find the area bounded by the curve y = x² and the line y = 4

The marginal cost and marginal revenue with respect to commodity of a firm are given by C'(x) = 8 + 6x and R'(x)= 24. Find the total Profit given that the total cost at zero output is zero.