Given \frac{\mathrm{d} y}{\mathrm{~d} x}=\cos x-x, \text { find } y .

Step-by-Step

Learn more on how do we answer questions.

We need to find a function which, when differentiated, yields \cos x − x. Differentiating sin x yields \cos x, while differentiating −x²/2 yields −x. Hence,

y=\int(\cos x-x) \mathrm{d} x=\sin x-\frac{x^2}{2}+c

where c is the constant of integration. Usually brackets are not used and the integral is written simply as \int \cos x-x d x.

Question: 13.11

Figure 13.13 illustrates the required area. From t...

Question: 13.10

(a) A graph of y = sin x between x = −π and x = π ...

Question: 13.9

Figure 13.11 illustrates the required area.
[latex...

Question: 13.8

\begin{aligned}\text { Area } & =\int_1...

Question: 13.7

(a) Let I stand for \int_1^2 x^2+1 d x[/la...

Question: 13.6

(a) Using the identities in Table 3.1 we find
[lat...

Question: 13.5

Powers of trigonometric functions, for example [l...

Question: 13.4

(a) \int x^2+9 \mathrm{~d} x=\int x^2 \math...

Question: 13.3

(a) From Table 13.1, we find \int x^n \mat...

Question: 13.2

From Table 10.1 we find
\frac{\mathrm{d}}{\...