Definite Integration
Definite Integration
nta_abhyas_2025
Grade 12
Question:
Let the value of integral is $I$, then, $I = \int_0^\pi (\cos 2x \cos 2^2 x \cos 2^3 x)dx$
Step-by-Step Solution
Key Concept: Using the property of definite integrals where $\int_0^a f(x)dx = \int_0^a f(a-x)dx$ to simplify the integral
We have $I = \int_0^\pi \cos 2x \cos 2^2 x \cos 2^3 x dx$. Using the property $f(x) = f(\pi - x)$, we apply the integration formula. Adding the equations, we get $2I = 0 \Rightarrow I = 0$.
Correct Answer: 0