Question: f(x) = $\int _ { 0 } ^ { x } \left( t ^ { 2 } - 1 \right) \cos t d t$, x ∈ (0, 2π).f(x) attains l...

Question

f(x) = $\int _ { 0 } ^ { x } \left( t ^ { 2 } - 1 \right) \cos t d t$ , x ∈ (0, 2π).f(x) attains local

maximum value at

Answer 1

f '(x) = (x² – 1) cosx Sign scheme of f '(x) is

clearly x = $\frac { \pi } { 2 }$ is the point of local maxima.

Question: f(x) = \(\int _ { 0 } ^ { x } \left( t ^ { 2 } - 1 \right) \cos t d t\), x ∈ (0, 2π).f(x) attains l...