integral of-cos((pit)/4)

解答

\int - cos (\frac{π t}{4}) d t

- \frac{4}{π} sin (\frac{π t}{4}) + C

求解步骤

\int - cos (\frac{π t}{4}) d t

提出常数:

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

= - \int cos (\frac{π t}{4}) d t

使用换元积分法

= - \int cos (u) \frac{4}{π} d u

提出常数:

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

= - \frac{4}{π} \cdot \int cos (u) d u

使用积分常见定则:

\int cos (u) d u = sin (u)

= - \frac{4}{π} sin (u)

u = \frac{π t}{4}

代回

= - \frac{4}{π} sin (\frac{π t}{4})

解答补常数

= - \frac{4}{π} sin (\frac{π t}{4}) + C

x \to - 2 lim (- x^{2} + 6 x - 8)

\int a arctan (b x) d x

x \to 1 lim (x^{2} + 4)

t an g e n t y = - 0.02 x^{2} - 0.6 x + 90

\frac{d}{d x} (\frac{1}{( x ^{2} + 1 ) ^{3}})