Pearson Edexcel IAL Mathematics P2.8.1 Evaluation of definite integrals

Practise evaluating definite integrals from expressions or related results, including constants, transformed functions, and exact or approximate values.

Exam points

substitute upper and lower limits into an antiderivative and subtract correctly
use a given integral value to calculate related integrals
form an equation from a definite integral to solve for an unknown constant k

[Maximum number: 3]

(a)

Using your answer to part (b) and making your method clear, estimate

[ 3 ]

(i)

$\int_{2}^{3.5}\left(2^{x}+2 x\right) \mathrm{d} x$

[ 2 ]

$\int_2^{3.5}(2^x+2x)\,dx=\int_2^{3.5}(2^x-2x+4x)\,dx$ $=2.34+[2x^2]_2^{3.5}$ =2.34+16.5=18.84

M1
A1ft

M1: Realises that the integral can be written as $\int_2^{3.5}(2^x-2x+4x)\,dx$ and integrates the 4x term.
A1ft: 2.34+16.5=18.84, following through on the answer to part (b); allow awrt 3 s.f.

(ii)

$\int_{2}^{3.5}\left(2^{x+1}-4 x\right) \mathrm{d} x$

[ 1 ]

B1 ft: For $2\times$ their answer to part (b), so $2\times2.34=4.68$ (awrt 3 s.f.; must be evaluated).
Note: Answer via repeated trapezium rule is permitted to score the B1 as long as the answer is twice their part (b).

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P2.8.1 - Evaluation of definite integrals question 1

Question (a)

Question (i)

Question (ii)