Definite integrals Quiz 1

Question 1

Evaluate $$\int_{0}^{1}{{{x}^{3}}-11{{x}^{2}}+7x-23dx}$$

Accepted Answer

$$\dfrac{-275}{12}$$

Answer

$$\dfrac{-275}{2}$$

Answer

$$\dfrac{-275}{7}$$

Answer

$$\dfrac{-275}{17}$$

Question 2

Evaluate $$\int_{0}^{1}{8{{x}^{7}}-13{{x}^{3}}+6x-5dx}$$

Accepted Answer

$$-4.25$$

Answer

$$4.75$$

Answer

$$-5.75$$

Answer

None of the above

Question 3

Evaluate $$\int_{0}^{1}{\ln (1+{{x}^{2}})dx}$$

Accepted Answer

$$\dfrac{2\ln (2)+\pi -4}{2}$$

Answer

$$\dfrac{\ln (2)+\pi -4}{4}$$

Answer

$$0$$

Answer

None of these

Question 4

Evaluate $$\int_{0}^{1}{{{\sin }^{-1}}(1-x)dx}$$

Accepted Answer

$$\dfrac{\pi }{2}-1$$

Answer

$$\dfrac{\pi }{2}$$

Answer

$$\pi -1$$

Answer

$$\pi -2$$

Question 5

Evaluate $$\int_{0}^{1}{{{\cos }^{-1}}(1-{{x}^{2}})dx}$$

Accepted Answer

$$\dfrac{1}{2}\left(-4\sqrt{2}+\pi +4\right)$$

Answer

$$\dfrac{\pi -{{2}^{\frac{5}{2}}}+4}{2}\pi$$

Answer

$$\dfrac{\pi -{{2}^{\frac{3}{2}}}+4}{2}$$

Answer

$$\pi -{{2}^{\frac{5}{2}}}$$