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# Edexcel A-level Maths Basics of integration The Fundamental Theorem of Calculus states that integration is the inverse process of differentiation. During differentiation, the constant terms of the function being differentiated will disappear. Thus, to account for this in integration, a constant is added to the integral. This constant is usually expressed as c and is called the constant of integration. The integral of a polynomial ax^n is given by ax^(n + 1)/(n + 1) + c, where c is the constant of integration. During differentiation, the constant terms of the function being differentiated will disappear. Thus, to account for this in integration, a constant is added to the integral. This constant is usually expressed as c and is called the constant of integration. Indefinite integrals do not have an evaluated constant of integration. They represent a family of functions which have the same derivative, and their only difference is the value of the constant of integration. # ✅

Demonstrate the Fundamental Theorem of Calculus using the following equation: y = 10sinx + 6x + 10. # ✅

A function is differentiated and then integrated. What is the result? # ✅

Integrate y = 10. # ✅

Given that the constant of integration is 5, find the integral of 5x⁴ + 27x². # ✅

What is the function of the velocity of the object whose acceleration is given by a = 20t + 50, where t is time in seconds? # ✅

Evaluate ∫10x + 8dx. # ✅

Given that the constant of integration is −4, evaluate ∫5x⁴ + 20xdx. # ✅

Given that the gradient of the graph is given by dy/dx = 10x + 10 and that at x = −1, y = −9, find the equation of the graph. # ✅

Solve the integral ∫4x + 32x⁷dx. # ✅

Two functions are found to have the same indefinite integral. Explain what this means.  Have you found the questions useful?