Title: MAT. Primitiva
Course: Matemàtiques de 3r d'ESO

Feedback shared by this category's questions, if right: La teva resposta és correcta.
Feedback shared by this category's questions, if partly right: La teva resposta és parcialment correcta.
Feedback shared by this category's questions, if wrong: La teva resposta és incorrecta.

- $$\displaystyle{\int \frac{f(x)}{f'(x)} dx =\ln |f(x)|+C}$$
- $$\displaystyle{\int \frac{f'(x)}{f(x)} dx =\ln |f(x)|+C}$$
- $$\displaystyle{\int \frac{f'(x)}{f(x)} dx =\frac{1}{2} (f(x))^2+C}$$
- $$\displaystyle{\int \frac{f(x)}{f'(x)} dx =\frac{1}{2} (f(x))^2+C}$$
- $$\displaystyle{\int \frac{f(x)}{f'(x)} dx =f(x)+C}$$
- $$\displaystyle{\int \frac{f'(x)}{f(x)} dx =f(x)+C}$$
- $$\displaystyle{\int \frac{f'(x)}{f(x)} dx =-\frac{1}{(f(x))^2}+C}$$
- $$\displaystyle{\int \frac{f(x)}{f'(x)} dx =-\frac{1}{(f(x))^2}+C}$$
- $$\displaystyle{\int \frac{f(x)}{f'(x)} dx =\ln |x|+C}$$
- $$\displaystyle{\int \frac{f'(x)}{f(x)} dx =\ln |x|+C}$$
A: $$\displaystyle{\int \frac{f'(x)}{f(x)} dx =\ln |f(x)|+C}$$

Q: $$\displaystyle{\int \cos x dx=}$$
A: sin x + C / sin x + K / sinx + C / sinx + K / sinx+C / sinx+K
Partly right: sinx (80%); sin x (80%)

Q: Si apliquem el canvi de variable $$x=g(t)$$

Llavors $$\displaystyle{\int f(x) dx=}$$
- $$\displaystyle{\int f(g(t)) dx}$$
- $$\displaystyle{\int f(g(t))dt}$$
- $$\displaystyle{\int f(g(t)) g'(t) dt}$$
- $$\displaystyle{\int g(t) f'(t) dt}$$
- $$\displaystyle{\int g(t) dt}$$
A: $$\displaystyle{\int f(g(t)) g'(t) dt}$$

Q: Si F(x) és primitiva de f(x) s'indica amb $$\int$$[...][...]= [...] +[...]
A: f(x); dx; F(x); C
Gap 1 offers: f(x); F(x); f'(x); F'(x); f
Gap 2 offers: df; dF; dx; dy; dC; C
Gap 3 offers: f(x); F(x); f'(x); F'(x); f; C
Gap 4 offers: x; y; f; F; C

Q: $$F(x)$$ és una primitiva de $$f(x)$$ si
- $$F'(x)=f(x)$$
- $$f'(x)=F(x)$$
- $$F'(x)-f'(x)=k$$
- $$F'(x)-f'(x)=0$$
- $$|F(x)|=f(x)$$
- $$\frac{F(x)}{f(x)}=k$$
- $$\frac{f(x)}{F(x)}=k$$
- $$F(f(x)))=F(x)$$
- $$F(f(x)))=x$$
- $$F(f(x)))=f(x)$$
A: $$F'(x)=f(x)$$

- $$\displaystyle{\int f(x) g'(x) dx=f(x) g(x)-\int f'(x) g(x) dx}$$
- $$\displaystyle{\int f'(x) g'(x) dx=f(x) g(x)-\int f'(x) g'(x) dx}$$
- $$\displaystyle{\int f(x) g'(x) dx=f(x) g(x)-\int f'(x) g'(x) dx}$$
- $$\displaystyle{\int f(x) g(x) dx=f'(x) g(x)-\int f(x) g'(x) dx}$$
- $$\displaystyle{\int f(x) g'(x) dx=f(x) g(x)+\int f'(x) g(x) dx}$$
- $$\displaystyle{\int f'(x) g'(x) dx=f(x) g(x)+\int f'(x) g'(x) dx}$$
- $$\displaystyle{\int f(x) g'(x) dx=f(x) g(x)+\int f'(x) g'(x) dx}$$
- $$\displaystyle{\int f(x) g(x) dx=f'(x) g(x)+\int f(x) g'(x) dx}$$
A: $$\displaystyle{\int f(x) g'(x) dx=f(x) g(x)-\int f'(x) g(x) dx}$$
Feedback: Fórmula d'intregració per parts:

Q: $$\displaystyle{\int x^n dx =}$$
- $$nx^{n-1} +C ~~~~~ \forall n \neq -1$$
- $$(n+1)x^{n+1} +C~~~~~\forall n \neq -1$$
- $$\frac{1}{n+1}x^{n+1} +C~~~~~\forall n \neq -1$$
- $$\frac{1}{n}x^{n-1} +C~~~~~\forall n \neq -1$$
- $$nx^{n-1} +C~~~~~\forall n \in \mathbb{Q}$$
- $$(n+1)x^{n+1} +C~~~~~\forall n \in \mathbb{Q}$$
- $$\frac{1}{n+1}x^{n-1} +C~~~~~\forall n \in \mathbb{Q}$$
- $$\frac{1}{n}x^{n-1} +C~~~~~\forall n \in \mathbb{Q}$$
- $$\ln x +C~~~~~\forall n \in \mathbb{Q}$$
- $$\ln x +C~~~~~si\,\,\,n=-1$$
- $$\ln x + C~~~~~ si\,\,\,n=1$$
A: $$\frac{1}{n+1}x^{n+1} +C~~~~~\forall n \neq -1$$; $$\ln x +C~~~~~si\,\,\,n=-1$$

- $$\displaystyle{\int (g(x))^n dx =\frac{1}{n+1}(g(x))^{n+1}+C}$$
- $$\displaystyle{\int (g(x))^n g'(x)dx =\frac{1}{n+1}(g(x))^{n+1}+C}$$
- $$\displaystyle{\int (g(x))^n g'(x)dx =n (g(x))^{n-1}+C}$$
- $$\displaystyle{\int (g(x))^n dx =n (g(x))^{n-1}+C}$$
- $$\displaystyle{\int (g(x))^n dx =(n+1) (g(x))^{n+1}+C}$$
- $$\displaystyle{\int (g(x))^n g'(x)dx =(n+1) (g(x))^{n+1}+C}$$
A: $$\displaystyle{\int (g(x))^n g'(x)dx =\frac{1}{n+1}(g(x))^{n+1}+C}$$

- $$\displaystyle{\int \cos g(x) \cdot g'(x)\,\, dx=\sin g(x) +C}$$
- $$\displaystyle{\int \cos g(x)\,\, dx=\sin g(x) +C}$$
- $$\displaystyle{\int \cos g(x) \cdot g'(x)\,\, dx=-\sin g(x) +C}$$
- $$\displaystyle{\int \cos g(x)\,\, dx=-\sin g(x) +C}$$
- $$\displaystyle{\int \cos g(x)\,\, dx=\sin g(x) \cdot \cos x+C}$$
- $$\displaystyle{\int \cos g(x)\,\, dx=-\sin g(x) \cdot \cos x+C}$$
A: $$\displaystyle{\int \cos g(x) \cdot g'(x)\,\, dx=\sin g(x) +C}$$

- $$\displaystyle{\int f(x)+g(x)\,\, dx=\int f(x)\,\, dx+\int g(x)\,\, dx}$$
- $$\displaystyle{\int k \cdot f(x)\,\, dx=k \cdot \int f(x)\,\, dx}$$
- $$\displaystyle{\int f(x)\cdot g(x)\,\, dx=\int f(x)\,\, dx\cdot \int g(x)\,\, dx}$$
- $$\displaystyle{\int \frac{f(x)}{g(x)}\,\, dx=\frac{\int f(x)\,\, dx}{\int g(x)\,\, dx}}$$
- $$\displaystyle{\left( \int f(x)\,\, dx \right)^2=\int (f(x))^2\,\, dx}$$
- $$\displaystyle{\int k \cdot f(x)\,\, dx=\int k\,\, dx \cdot \int f(x)\,\, dx}$$
A: $$\displaystyle{\int f(x)+g(x)\,\, dx=\int f(x)\,\, dx+\int g(x)\,\, dx}$$; $$\displaystyle{\int k \cdot f(x)\,\, dx=k \cdot \int f(x)\,\, dx}$$