# Can I say that Integration can be equal to the formula of finding the area of a right triangle?

Let us have a certain function like $$f(x)=x$$

In the world of integration, can I say that $$\int_{0}^bxdx=\frac{1}{2}(b)(f(b))$$? Because if you look at graph of function x, it would look like something 45° right triangle (though we can probably change its angle using the trig func $$\tan$$ and multiplying it by x like this $$f(x)=x\tan(s)$$ or in integration $$\int_{0}^bx\tan(s)dx=\frac{1}{2}(b)(b\tan(s))$$ or making it more complicated $$\int_{a}^bx\tan(s°)dx=(\frac{1}{2}(b)(b\tan(s°)))-\frac{1}{2}(a)(f(a))$$ where s is your/the preferred angle.

• Yes, but this will only work if you’re integrating lines through the origin, of course. – symplectomorphic Jun 11 at 5:33
• Further to @symplectomorphic's comment, an integral under a line, neither end on the $y$-axis, is a trapezium. This is the basis of the trapezium rule. – J.G. Jun 11 at 5:54