Integration
GCE Further Mathematics

(a) Find the integral ∫(3x² + 4x - 5) dx. (b) Evaluate ∫₁³ (2x³ - 6x + 1) dx. (c) A curve passes through the point (2, 7) and its gradient function is given by dy/dx = 3x² - 4x + 1. Find the equatio…

(a) Using integration by substitution or otherwise, find ∫ x(2x² + 3)⁴ dx. (b) (i) Sketch the curves y = x² and y = 4x - x² on the same axes, indicating clearly their points of intersection. (ii)…

Evaluate $\int_{0}^{2} (x^2 + 1)\, dx$

Find $\int \frac{1}{5x+3}\, dx$

Evaluate $\int x e^{x}\, dx$

Evaluate ∫(3x² + 2x - 5) dx

Evaluate $\int_{1}^{e} \frac{\ln x}{x}\, dx$

Using the substitution $u = x^2 + 1$, evaluate $\int_{0}^{2} \frac{x}{x^2+1}\, dx$

Find the area enclosed between the curve $y = x^2 - 4$ and the x-axis

Find $\int \sin^2 x\, dx$

Find ∫cos(4x) dx