Chhaya Mathematics- Indefinite Integral [Part-2]
SN Dey Integration Solutions | The Math Fellow 3. Using the definition of integration, find \(y\) in terms of \(x\). 3(i) \(\dfrac{dy}{dx}=3x^2+2\) Given \(\dfrac{dy}{dx}=3x^2+2\). Integrate both sides: \[ y=\int(3x^2+2)\,dx = 3\int x^2dx + 2\int dx = 3\cdot\frac{x^3}{3} + 2x + C = x^3 + 2x + C. \] \(\boxed{y=x^3+2x+C}\) 3(ii) \(dy=(ax+b)dx\) Integrate: \[ y=\int (ax+b)dx … Read more