integral from x to 1 of (1-y)cos^2(z-y)

解答

\int_{x}^{1} (1 - y) cos^{2} (z - y) d z

(1 - y) \frac{1}{2} (- x + 1 + \frac{1}{2} (sin (2 (- y + 1)) - sin (2 (- y + x))))

求解步骤

\int_{x}^{1} (1 - y) cos^{2} (z - y) d z

提出常数:

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

= (1 - y) \cdot \int_{x}^{1} cos^{2} (- y + z) d z

\int_{x}^{1} cos^{2} (- y + z) d z = \frac{1}{2} (- x + 1 + \frac{1}{2} (sin (2 (- y + 1)) - sin (2 (- y + x))))

= (1 - y) \frac{1}{2} (- x + 1 + \frac{1}{2} (sin (2 (- y + 1)) - sin (2 (- y + x))))

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