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受欢迎的微积分 >

integral from 3 to 7 of 4cos(2x+3)

解答

\int_{3}^{7} 4 cos (2 x + 3) d x

解答

2 (sin (17) - sin (9))

+1

十进制

- 2.74703 \dots

求解步骤

\int_{3}^{7} 4 cos (2 x + 3) d x

提出常数:

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

= 4 \cdot \int_{3}^{7} cos (2 x + 3) d x

使用换元积分法

= 4 \cdot \int_{9}^{17} cos (u) \frac{1}{2} d u

提出常数:

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

= 4 \cdot \frac{1}{2} \cdot \int_{9}^{17} cos (u) d u

使用积分常见定则:

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

= 4 \cdot \frac{1}{2} [sin (u)]_{9}^{17}

化简

4 \cdot \frac{1}{2} [sin (u)]_{9}^{17} : 2 [sin (u)]_{9}^{17}

= 2 [sin (u)]_{9}^{17}

带入上下限计算后得:

sin (17) - sin (9)

= 2 (sin (17) - sin (9))

作图

流行的例子

integral from 2 to 3 of xe^{-x}

\int_{2}^{3} x e^{- x} d x

integral from 1 to 7 of ln(t)

\int_{1}^{7} ln (t) d t

integral from 0 to 1 of 70x(2x^2+1)^4

\int_{0}^{1} 70 x (2 x^{2} + 1)^{4} d x

integral from 1 to n of 1/x

\int_{1}^{n} \frac{1}{x} d x

integral from-3 to 0 of sqrt(1-x)

\int_{- 3}^{0} 1 - x d x