# StudySquare

# OCR A-level Maths Basics of integration

This page covers the following topics:

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.

# 1

# ✅

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

# 5

# ✅

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

# 8

# ✅

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.

# 10

# ✅

Two functions are found to have the same indefinite integral. Explain what this means.

End of page