Consider the function \( f(x)=\frac{2}{x^{2}}-\frac{7}{x^{7}} \). Let \( F(x) \) be the antiderivative of \( f(x) \) with \( F(1)=0 \). Then \( F(x)= \)

1. Calcule la dorivada de les sisuiantos tunci a). \( f(x)=\left(3 x-x^{3}\right)^{100} \)

Evaluate the improper integral: \( \int_{1}^{\infty} \frac{1}{x^2} \, dx \)

Consider the parametric curve \( x=\cos \theta \) and \( y=\sin \theta \). Determine whether this curve is concave up, down, or neither at \( \theta=\frac{\pi}{6} \) A) upward B) downward C) neither D) All answers a b

¿Cuál es la longitud de la curva paramétrica \( r(x)=\left(4 t^{3}+7 t, 3 t^{2}-1,2 t^{3}-5 t^{2}+4 t\right. \) en el intervalo \( [0,2] \) ?

Al resolver la integral doble \( \int_{1}^{2} \int_{1-x}^{\sqrt{x}} x^{2} y d y d x \) obtenemos: a. 402 b. 170 c. 170 d. \( 163 / 120 \)