Integral Chasing
Below is a selection of integrals, some of which you can't do directly and some that require the use of other mathematical skills.
Can you find the missing positive numbers $a$ to $d$?
$$\text{(1)} \ \int_a^5 10x+3 \ \text{d}x = 114$$
$$\text{(2)} \ \int_{2a}^9 b\sqrt{x}+\dfrac{a}{\sqrt{x}}\ \text{d}x=42$$
$$\text{(3)} \ \int_{\frac{1}{2}}^1 \dfrac{1}{x^5}-\dfrac{1}{x^2} \ \text{d}x=\dfrac{c+1}{4}$$
$$\text{(4)} \ \int^{c+2}_6 x^{\frac{b}{a}}\left(\sqrt{x}-\dfrac{1}{\sqrt{x}}\right) \ \text{d}x=ab^ad^a$$
Underground Mathematics is hosted by Cambridge Mathematics. The project was originally funded by a grant from the UK Department for Education to provide free web-based resources that support the teaching and learning of post-16 mathematics.
Visit the site at undergroundmathematics.org to find more resources, which also offer suggestions, solutions and teacher notes to help with their use in the classroom.
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