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1.8.4 Evaluating definite integrals

How can you check that F(x)F(x)F(x) is an antiderivative of f(x)f(x)f(x)?

A

A region above the xxx-axis contributes positively, while a region below contributes negatively to a definite integral.

B

Reversing the limits gives ∫baf(x) dx=−∫abf(x) dx\boxed{\int_b^a f(x)\,dx=-\int_a^b f(x)\,dx}∫ba​f(x)dx=−∫ab​f(x)dx​, while equal limits give ∫aaf(x) dx=0\int_a^a f(x)\,dx=0∫aa​f(x)dx=0.

C

For a<c<ba<c<ba<c<b, the splitting property is ∫abf(x) dx=∫acf(x) dx+∫cbf(x) dx\boxed{\int_a^b f(x)\,dx=\int_a^c f(x)\,dx+\int_c^b f(x)\,dx}∫ab​f(x)dx=∫ac​f(x)dx+∫cb​f(x)dx​.

D

Differentiate F(x)F(x)F(x) and check that F′(x)=f(x)F'(x)=f(x)F′(x)=f(x).

1.8.4 Evaluating definite integrals Flashcards

  1. A Level
  2. /Maths
  3. /1.8.4 Evaluating definite integrals

Flashcards for OCR A Level Maths 1.8.4 Evaluating definite integrals, covering the key formulae, methods and definitions you need to recall for Paper 1, Paper 2 and Paper 3. 21 cards, matched to the OCR A Level Maths (H240) specification. Recall questions account for roughly 50% of marks at A Level Maths, so these target the marks you can secure before the paper starts.