In calculus, one often comes across the task of finding the integral, a process that essentially determines the antiderivative, or primitive, of a function. This task is tantamount to finding the area beneath a curve, which signifies the cumulative change over a specific interval. There are several methods to approach this, including substitution, integration by parts, partial fractions, or numerical integration.
| Topic | Problem | Solution |
|---|---|---|
| None | Determine the integral of the given function: $\… | Let's start by using the substitution method. We let \(u = t^4 - 6\). |
| None | Find the integral. \[ \int\left(9 x^{2}-4 x+5\rig… | The integral of a function is found by applying the power rule of integration, which states that th… |
| None | Find $\int\left(4 x^{5}+2 x^{6}\right) d x$ | Split the integral into two parts: \(\int 4x^5 dx\) and \(\int 2x^6 dx\). |
| None | \( \int(\sqrt[3]{x} \cdot \sqrt[2]{x}) x d x \) | \( = \int(x^{\frac{1}{3}} \cdot x^{\frac{1}{2}}) dx \) |