Mathematics (AS)·Integration · NSSCAS 2.5.1
Integrating exponentials, 1/(ax+b) & trig
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In this lesson you will learn to integrate e to the power a x plus b, one over a x plus b, and the trig functions sine, cosine and secant squared of a x plus b — all by running differentiation in reverse. You will build a reference card of standard integrals, divide by a every time, remember the modulus in the log, and watch the sign on the cosine. You will also meet the double-angle trick that lets you integrate cos squared x and sin squared x. By the end you can read each integral straight off the card and evaluate a definite integral to three significant figures.
What you'll learn in this lesson
By the end you should be able to (NSSCAS Mathematics (AS) 2.5.1):
- Apply reverse differentiation to integrate e^(ax+b), 1/(ax+b), sin(ax+b), cos(ax+b) and sec²(ax+b), dividing by a for the linear inside (substitution not required).
- Use trigonometric relationships such as the double-angle formulae to integrate functions like cos²x and sin²x.
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