# Definite integrals. Fundamental Theorem of Calculus

 1. (20 p.) Find the area bounded by the lines $$x=1$$, $$x=3$$, the $$x$$-axis, and the parabola $$y=x^2+3$$.    A    $$\frac{44}3$$    B    $$18\sqrt 6+11$$    C    $$\frac{251}6$$    D    $$15$$    E    $$43$$    N

 2. (20 p.) Find the integral $\int_3^9 \left(x^2-3\right)\,dx.$    A    243    B    216    C    $$\frac{185}3$$    D    $$\frac{4\sqrt 3}3$$    E    $$2\pi$$    N

 3. (20 p.) Find the area bounded by the lines $$x=1$$, $$x=5$$, the $$x$$-axis, and the parabola $$y=x^2+2x+7$$.    A    $$\frac{81}{2}+\sqrt{17}$$    B    $$23\sqrt 5+7$$    C    $$\frac{521}6$$    D    $$95$$    E    $$\frac{280}3$$    N

 4. (20 p.) Evaluate the integral $\int_2^{8}\left(\frac1x+x^2\right)\,dx.$    A    $$2\sqrt{15}+820$$    B    $$\ln 4+\frac{594}3$$    C    $$\ln 4+168$$    D    $$e^3+28$$    E    $$420$$    N

 5. (20 p.) Evaluate the integral $\int_{-1}^1 \frac{x^2}{1+x^2}\,dx.$    A    $$2$$    B    $$2-\frac{\pi}2$$    C    $$\frac{3}4$$    D    $$2\sqrt 5$$    E    $$0$$    N

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