Definite Integration
Absolute Value Integral with Even-Function Property
nta_pyq_2023_apr
Grade 12
Question:
If $\displaystyle\int_{-0.15}^{0.15}|100x^2-1|\,dx=\dfrac{k}{3000}$, then $k$ is equal to _____.
Step-by-Step Solution
Key Concept: The integrand is even, so use $2\int_0^{0.15}|100x^2-1|\,dx$. Split at $x=0.1$ (where $100x^2=1$): on $[0,0.1]$ integrand $=1-100x^2$; on $[0.1,0.15]$ integrand $=100x^2-1$.
$k=575$.
Correct Answer: 575