Diberi bahawa \( \int_{1}^{2 f}(\mathrm{x}) \mathrm{dx}=11 \), cari Given that \( \int_{1}^{2} 8 \mathrm{f}(\mathrm{x}) \mathrm{dx}=11 \), find (i) \( \int_{1}^{2} 4 f(x) d x \), (ii) nilai k jika \( \int_{1}^{2}[10 \mathrm{f}(\mathrm{x})-\mathrm{kx}] \mathrm{dx}=10 \). the value of \( k \) if \( \int_{1}^{2}[10 f(x)-k x] d x=10 \).

A solid is formed with triangular cross-sections where each triangle's base is defined by the equation \(y = x^2\) on interval \([0, 2]\). What is the volume of this solid?

Application 3: Simplifier les expressions suivantes: \( \begin{array}{ll}A=\ln (\sqrt{3})+\ln 3-\ln 9 & ; \\ C=\ln \left(\frac{1}{3}\right)+\ln \left(\frac{3}{5}\right)+\ln \left(\frac{5}{7}\right)+\ln \left(\frac{7}{9}\right) & ;\end{array} \quad D=\ln (\sqrt[3]{2}-\ln 16 \)

\( \int _{0}^{\frac{\pi }{2}}\frac{1}{2+\cos (x)} d x \)

(iv) In integral equation of the form \( \int_{0}^{1} \frac{F(u) d u}{(t-u)^{n}}=G(t) \) is called. (a) Exact equation (b) Convolution type (c) Integro-differential equation (d) Abel's equation

Calcula el área entre las curvas \( y = x^3 - 3x \) y \( y = x + 1 \) sobre el intervalo definido por sus intersecciones.