Title: MAT. Càlcul de long., superf. i volums per integració
Course: Matemàtiques de 3r d'ESO

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Q: El volum del cos de revolució engendrat per la funció $$f$$ en l'interval $$[a,b]$$, quan gira al voltant de l'eix x, és
- $$\displaystyle{\pi \int_a^b (f(x))^2 dx}$$
- $$\displaystyle{\pi \int_a^b f(x) dx}$$
- $$\displaystyle{\pi \int_a^b f(x^2) dx}$$
- $$\displaystyle{\pi \int_a^b f(x) dx^2}$$
- $$\displaystyle{\pi \int_a^b \sqrt{1-(f'(x))^2} dx}$$
- $$\displaystyle{\int_a^b \sqrt{1-(f'(x))^2} dx}$$
- $$\displaystyle{\pi \int_a^b (1-(f'(x))^2) dx}$$
- $$\displaystyle{\int_a^b (1-(f'(x))^2) dx}$$
- $$\displaystyle{\pi \int_a^b \sqrt{1+(f'(x))^2} dx}$$
- $$\displaystyle{\int_a^b \sqrt{1+(f'(x))^2} dx}$$
- $$\displaystyle{\pi \int_a^b (1+(f'(x))^2)) dx}$$
- $$\displaystyle{\int_a^b (1+(f'(x))^2) dx}$$
- $$\displaystyle{\pi \int_a^b \sqrt{1-(f(x))^2} dx}$$
- $$\displaystyle{\int_a^b \sqrt{1-(f(x))^2} dx}$$
- $$\displaystyle{\pi \int_a^b (1-(f(x))^2) dx}$$
- $$\displaystyle{\int_a^b (1-(f(x))^2) dx}$$
- $$\displaystyle{\pi \int_a^b \sqrt{1-(f(x))^2} dx}$$
- $$\displaystyle{\int_a^b \sqrt{1-(f(x))^2} dx}$$
- $$\displaystyle{\pi \int_a^b (1-(f(x))^2) dx}$$
- $$\displaystyle{\int_a^b (1-(f(x))^2) dx}$$
- $$\displaystyle{2\pi \int_a^b f(x) \sqrt{1+(f'(x))^2} dx}$$
A: $$\displaystyle{\pi \int_a^b (f(x))^2 dx}$$

Q: La longitud de la corba $$f$$ en l'interval $$[a,b]$$ és
- $$\displaystyle{\pi \int_a^b (f(x))^2 dx}$$
- $$\displaystyle{\pi \int_a^b f(x) dx}$$
- $$\displaystyle{\pi \int_a^b f(x^2) dx}$$
- $$\displaystyle{\pi \int_a^b f(x) dx^2}$$
- $$\displaystyle{\pi \int_a^b \sqrt{1-(f'(x))^2} dx}$$
- $$\displaystyle{\int_a^b \sqrt{1-(f'(x))^2} dx}$$
- $$\displaystyle{\pi \int_a^b (1-(f'(x))^2) dx}$$
- $$\displaystyle{\int_a^b (1-(f'(x))^2) dx}$$
- $$\displaystyle{\pi \int_a^b \sqrt{1+(f'(x))^2} dx}$$
- $$\displaystyle{\int_a^b \sqrt{1+(f'(x))^2} dx}$$
- $$\displaystyle{\pi \int_a^b (1+(f'(x))^2) dx}$$
- $$\displaystyle{\int_a^b (1+(f'(x))^2) dx}$$
- $$\displaystyle{\pi \int_a^b \sqrt{1-(f(x))^2} dx}$$
- $$\displaystyle{\int_a^b \sqrt{1-(f(x))^2} dx}$$
- $$\displaystyle{\pi \int_a^b (1-(f(x))^2) dx}$$
- $$\displaystyle{\int_a^b (1-(f(x))^2) dx}$$
- $$\displaystyle{\pi \int_a^b \sqrt{1-(f(x))^2} dx}$$
- $$\displaystyle{\int_a^b \sqrt{1-(f(x))^2} dx}$$
- $$\displaystyle{\pi \int_a^b (1-(f(x))^2) dx}$$
- $$\displaystyle{\int_a^b (1-(f(x))^2) dx}$$
A: $$\displaystyle{\int_a^b \sqrt{1+(f'(x))^2} dx}$$

Q: L'àrea exterior del cos de revolució engendrat per la funció $$f$$ en l'interval $$[a,b]$$, quan gira al voltant de l'eix x, és
- $$\displaystyle{\pi \int_a^b (f(x))^2 dx}$$
- $$\displaystyle{\pi \int_a^b f(x) dx}$$
- $$\displaystyle{\pi \int_a^b f(x^2) dx}$$
- $$\displaystyle{\pi \int_a^b f(x) dx^2}$$
- $$\displaystyle{\pi \int_a^b \sqrt{1-(f'(x))^2} dx}$$
- $$\displaystyle{\int_a^b \sqrt{1-(f'(x))^2} dx}$$
- $$\displaystyle{\pi \int_a^b (1-(f'(x))^2) dx}$$
- $$\displaystyle{\int_a^b (1-(f'(x))^2) dx}$$
- $$\displaystyle{\pi \int_a^b \sqrt{1+(f'(x))^2} dx}$$
- $$\displaystyle{\int_a^b \sqrt{1+(f'(x))^2} dx}$$
- $$\displaystyle{\pi \int_a^b (1+(f'(x))^2)) dx}$$
- $$\displaystyle{\int_a^b (1+(f'(x))^2) dx}$$
- $$\displaystyle{\pi \int_a^b \sqrt{1-(f(x))^2} dx}$$
- $$\displaystyle{\int_a^b \sqrt{1-(f(x))^2} dx}$$
- $$\displaystyle{\pi \int_a^b (1-(f(x))^2) dx}$$
- $$\displaystyle{\int_a^b (1-(f(x))^2) dx}$$
- $$\displaystyle{\pi \int_a^b \sqrt{1-(f(x))^2} dx}$$
- $$\displaystyle{\int_a^b \sqrt{1-(f(x))^2} dx}$$
- $$\displaystyle{\pi \int_a^b (1-(f(x))^2) dx}$$
- $$\displaystyle{\int_a^b (1-(f(x))^2) dx}$$
- $$\displaystyle{2\pi \int_a^b f(x) \sqrt{1-(f'(x))^2} dx}$$
- $$\displaystyle{2\pi \int_a^b f(x) \sqrt{1+(f'(x))^2} dx}$$
- $$\displaystyle{2\pi \int_a^b (f(x))^2 \sqrt{1+(f'(x))^2} dx}$$
- $$\displaystyle{2\pi \int_a^b f(x) \sqrt{1+f'(x)} dx}$$
- $$\displaystyle{\int_a^b f(x) \sqrt{1+(f'(x))^2} dx}$$
A: $$\displaystyle{2\pi \int_a^b f(x) \sqrt{1+(f'(x))^2} dx}$$