Let \( H(x)=\int_{0}^{x} \sqrt{64-t^{2}} d t \), for \( -8 \leq x \leq 8 \) a. Evaluate \( H(0) \) b. Evaluate \( H^{\prime}(3) \) c. Evaluate \( H^{\prime}(8) \) d. Use geometry to evaluate \( H(8) \) e. Find the value of \( s \) such that \( H(x)=s H(-x) \).

By using Newton-Raphson Method, determine the root for \( x^{3}+2 x^{2}-1=0 \). Given \( x_{0}=0.5 \). Give the answer correct to four decimal places. Dengan mengomenan

Calcule \( \int \frac{x^{4} - 5x^{2} + 6}{x-2} \,dx \) aplicando o método de divisão longa.

اجد التكامل غير المحدود للدالة \( f(x) = 3x^2 \).

Solve the following first order differential equations. \( \frac{d y}{d x}=4 x^{3}-8 x+7 \) bena tambah \( x \frac{d y}{d x}=5 x^{3}+4 \)

integral \( \int_{0}^{1} \int_{e^{y}}^{e} \frac{x}{\ln x} d x d y \) (by