Scaling Factor in Definite Integrals
Let \(f(x) = x^2\) be continuous on the interval \([0, 3]\). Using the property of constant multiples in definite integrals, evaluate \(\int_{0}^{3} 4x^2\,dx\).
Differentiating a Polynomial with Constant Multipliers
Differentiate the function \(f(x) = 5x^4 – 2x^3 + 7\) with respect to \(x\).
Differentiation Using Sum and Constant Multiple Rules
Differentiate the function \( f(x) = 3x^2 + 5 \) using the sum and constant multiple rules.
Derivative of a Radical Function with Polynomial Terms
Differentiate the function \(f(x) = x^{3/2} + 2x^{1/2}\) with respect to \(x\).