integral from 0 to pi/4 of 3/(cos^2(x))

解

\int_{0}^{\frac{π}{4}} \frac{3}{cos ^{2} ( x )} d x

3

解答ステップ

\int_{0}^{\frac{π}{4}} \frac{3}{cos ^{2} ( x )} d x

定数を除く:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 3 \cdot \int_{0}^{\frac{π}{4}} \frac{1}{cos ^{2} ( x )} d x

共通積分を使用する:

\int \frac{1}{cos ^{2} ( x )} d x = tan (x)

= 3 [tan (x)]_{0}^{\frac{π}{4}}

限度を計算する:

1

= 3 \cdot 1

簡素化

= 3