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

Find the area of the region bounded by the line x − 2y − 12 = 0 , the y-axis and the lines y = 2, y = 5.

Find the area of the region bounded by the parabola \(y=4{ - }x^{ 2 }\) , x −axis and the lines x = 0, x = 2.

Find the area bounded by y = x between the lines x = −1 and x = 2 with x -axis.

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 circle whose center is at the origin and the radius is a units.

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

The demand function of a commodity is y = 36 − x². Find the consumer’s surplus for y₀ = 11

Find the producer’s surplus defined by the supply curve g(x) = 4x + 8 when x_o= 5.

The demand and supply function of a commodity are p_d = 18− 2x − x² and p_s = 2x − 3 . Find the consumer’s surplus and producer’s surplus at equilibrium price.