利用定积分定义计算积分$\int_{a}^{b} x dx $
A: $\frac{1}{2}(b^2 -a^2)$
B: $\frac{1}{2}$
C: $\frac{1}{2}b^2 $
D: $\frac{1}{2}(a^2 - b^2)$
A: $\frac{1}{2}(b^2 -a^2)$
B: $\frac{1}{2}$
C: $\frac{1}{2}b^2 $
D: $\frac{1}{2}(a^2 - b^2)$
举一反三
- 1. 利用定积分定义计算积分$\int_{a}^{b} x dx $ A: $\frac{1}{2}(b^2 -a^2)$ B: $\frac{1}{2}$ C: $\frac{1}{2}b^2 $ D: $\frac{1}{2}(a^2 - b^2)$
- 积分\(\int_0^1 (x\sin\frac{1}{x^2} - \frac{1}{x}\cos\frac{1}{x^2})dx\) (不计算积分, 由判别法直接判断)
- 积分$\int_0^1 x \arctan xdx=$（）。 A: $\frac{\pi}{4}+\frac{1}{2}$ B: $\frac{\pi}{4}$ C: $\frac{\pi}{4}-\frac{1}{2}$ D: $\frac{1}{2}$
- For the integral $\int_0^{+\infty}\frac{dx}{(x^2+p^2)(x^2+q^2)}$, which of the following statements are CORRECT? A: $\frac{1}{q^2-p^2}[\frac{1}{p}-\frac{1}{q}]\frac{\pi}{2},p>0 \ q>0;$ B: $\frac{1}{q^2-p^2}[\frac{1}{q}+\frac{1}{p}]\frac{\pi}{2}, -p>0 \ -q>0;$ C: $\frac{1}{q^2-p^2}[\frac{1}{p}-\frac{1}{q}]\frac{\pi}{2}, p>0 \ -q>0;$ D: $\frac{1}{p^2-q^2}[\frac{1}{q}+\frac{1}{p}]\frac{\pi}{2}, -p>0 \ q>0.$
- Solve $\int_{-\frac{1}{2}}^1{1-x^2}dx=$? A: $\frac{\pi}{3}+\frac{\sqrt{3}}{8}$. B: $\frac{\pi}{2}$. C: $\frac{\pi}{6}+\frac{\sqrt{3}}{4}$. D: $\frac{\pi}{4}$.