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Tính giá trị

\frac{x ^{2}}{2} + С

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Lấy vi phân theo x

x

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Bài kiểm tra

\int x d x

Các bài toán tương tự từ Tìm kiếm web

\oint x d x

over a particular curve

C

https://math.stackexchange.com/questions/1788885/evaluate-oint-x-dx-over-a-particular-curve-c

The usual orientation is counter-clockwise so the path

C

, a triangle, would consist of the line segments from

(0, 0)

(1, 0)

(1, 0)

(0, 1)

and finally from

(0, 1)

(0, 0)

How do you evaluate the definite integral

\int 2 x d x

https://socratic.org/questions/how-do-you-evaluate-the-definite-integral-int-2x-dx-from-0-1

= 1

Explanation: First let us find the indefinite integral

\int 2 x d x

\int 2 x d x = x^{2} + C

How do you evaluate the definite integral

\int (5 x) d x

https://socratic.org/questions/how-do-you-evaluate-the-definite-integral-int-5x-dx-from-0-3

\frac{4 5}{2}

\int_{0}^{3} 5 x d x = 5 \int_{0}^{3} x d x = \frac{5}{2} x^{2} ∣_{x = 0}^{x = 3} = \frac{4 5}{2}

How do you use limits to evaluate

\int 8 x d x

https://socratic.org/questions/how-do-you-use-limits-to-evaluate-int-8xdx-from-0-2

Evaluating an integral using limits will give you the formula:

\int_{a}^{b} f (x) d x = n \to \infty lim i = 1 \sum n f (x_{i}) \cdot Δ x

Fake proof that

\frac{e ^{x} - 1}{e ^{x} + 1} = e^{x}

, via integrating

s e c h x

https://math.stackexchange.com/questions/1836980/fake-proof-that-fracex-1ex1-ex-via-integrating-operatornamesech

2 arctan (\frac{e ^{x} - 1}{e ^{x} + 1}) = 2 (arctan (e^{x}) - \frac{π}{4}) = 2 arctan (e^{x}) + C^{'}

. The results differ by a constant.

Notation: Why write the differential first?

https://math.stackexchange.com/q/387572

When you have a lot of integrals, particularly with limits, it can be very helpful at times to be able to tell at a glance which integral is over which variable.

\int_{0}^{1} \int_{2}^{3} f (x, y) d x d y

Chia sẻ

Đã sao chép vào bảng tạm

\frac{x^{2}}{2}

Vì \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} k\neq -1, thay thế \int x\mathrm{d}x bằng \frac{x^{2}}{2}.

\frac{x^{2}}{2}+С

Nếu F\left(x\right) là nguyên hàm của f\left(x\right) thì tập hợp mọi nguyên hàm của f\left(x\right) sẽ được tính bằng F\left(x\right)+C. Vì vậy, hãy thêm hằng số tích phân C\in \mathrm{R} vào kết quả.

Ví dụ

Phương trình bậc hai

x^{2} - 4 x - 5 = 0

4 sin θ cos θ = 2 sin θ

Phương trình tuyến tính

y = 3 x + 4

699 * 533

[2534] [2 - 1 0135]

Phương trình đồng thời

{8 x + 2 y = 46 7 x + 3 y = 47

\frac{d}{d x} \frac{( 3 x ^{2} - 2 )}{( x - 5 )}

\int_{0}^{1} x e^{- x^{2}} d x

x \to - 3 lim \frac{x ^{2} - 9}{x ^{2} + 2 x - 3}