1.По готовому чертежу найти площадь заштрихованной фигуры.

The image shows a graph of a function y=f(x) with a shaded area. The x-axis has points marked at -2, 0, and 1. The y-axis has a point marked at 5, which appears to be the maximum value of the function. The shaded area is bounded by the curve y=f(x), the x-axis, and the vertical lines x=-2 and x=1. Without the explicit function definition or more information about the shape of the curve, the exact area cannot be calculated. However, if we assume the curve is a parabola symmetric about the y-axis with its vertex at (0,5) and passing through (-2,0) and (2,0), the function could be of the form $$f(x) = a(x-h)^2 + k$$. Given the vertex is at (0,5), $$h=0$$ and $$k=5$$, so $$f(x) = ax^2 + 5$$. Since it passes through (-2,0), $$0 = a(-2)^2 + 5$$, which gives $$4a = -5$$, so $$a = -5/4$$. Thus, $$f(x) = -5/4 x^2 + 5$$. The area of the shaded region is the integral of $$f(x)$$ from -2 to 1: $$\int_{-2}^{1} (-5/4 x^2 + 5) dx = [-5/12 x^3 + 5x]_{-2}^{1} = (-5/12(1)^3 + 5(1)) - (-5/12(-2)^3 + 5(-2)) = (-5/12 + 5) - (40/12 - 10) = (-5/12 + 60/12) - (40/12 - 120/12) = 55/12 - (-80/12) = 55/12 + 80/12 = 135/12 = 45/4 = 11.25$$.