Tính chất của tích phân và một số ví dụ

Câu 1

1đ

$\int_{-2}^{-1}\dfrac{1}{x}\text{d}x=\ln\left|x\right| \Big|_{-2}^{-1}=$

\ln 2

.

-\ln 2

.

0

.

Câu 2

1đ

$\int_0^{2\pi}\left|\sin x\right|\text{d}x=$

\int_0^{2\pi}\sin x\text{d}x+\int_0^{2\pi}\left(-\sin x\right)\text{d}x

.

\int_0^{\pi}\left(-\sin x\right)\text{d}x+\int_{\pi}^{2\pi}\sin x\text{d}x

.

\int_0^{2\pi}\left(-\sin x\right)\text{d}x+\int_0^{2\pi}\sin x\text{d}x

.

\int_0^{\pi}\sin x\text{d}x+\int_{\pi}^{2\pi}\left(-\sin x\right)\text{d}x

.

Câu 3

1đ

$\int_0^{2\pi}\sqrt{1-\cos2x}\text{d}x$	$=$	$\sqrt{2}\int_0^{2\pi}\left\|\sin x\right\|\text{d}x$
	$=$	$\sqrt{2}\left(\int_0^{\pi}\sin x\text{d}x-\int_{\pi}^{2\pi}\sin x\text{d}x\right)$
	$=$
	$=$

4\sqrt{2}

\sqrt2\left[\left(-\cos x\right)\Big|_0^{\pi}-\left(-\cos x\right)\Big|_{\pi}^{2\pi}\right]

-4\sqrt{2}

0

\sqrt2\left(\cos x\Big|_0^{\pi}-\cos x\Big|_{\pi}^{2\pi}\right)

(Kéo thả hoặc click vào để điền)

Câu 4

1đ

$\int_0^{2\pi}\sqrt{1-\cos2x}\text{d}x$	$=$	$\sqrt{2}\int_0^{2\pi}\left\|\sin x\right\|\text{d}x$
	$=$	$\sqrt{2}\left(\int_0^{\pi}\sin x\text{d}x-\int_{\pi}^{2\pi}\sin x\text{d}x\right)$
	$=$
	$=$

4\sqrt{2}

\sqrt2\left[\left(-\cos x\right)\Big|_0^{\pi}-\left(-\cos x\right)\Big|_{\pi}^{2\pi}\right]

-4\sqrt{2}

0

\sqrt2\left(\cos x\Big|_0^{\pi}-\cos x\Big|_{\pi}^{2\pi}\right)

(Kéo thả hoặc click vào để điền)

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