Sec 4 A-Math Integration topical questions

Find ∫(6x² − 4x + 1) dx.

Find ∫(4x³ − 6/x²) dx.

Evaluate ∫₀²(3x² + 2x) dx.

Find ∫(2x + 3)⁵ dx.

Evaluate ∫₀^(π/2)(sin x + cos x) dx.

Find the area of the region bounded by the curve y = 4 − x² and the x-axis.

Find the total area of the region between y = x² − 4 and the x-axis from x = 0 to x = 3.

Find the area of the region enclosed by the curve y = 9 − x² and the line y = x + 3.

The region R is bounded by the curve y = eˣ, the y-axis, the x-axis and the line x = 2. Find the exact area of R and its value correct to 3 significant figures.

The curve y = x(6 − x) crosses the x-axis at O and at P. (a) Find the coordinates of P and of the maximum point of the curve. (b) Find the area of the region bounded by the curve and the x-axis, and verify it equals (2/3) × (base OP) × (maximum height).