Question

exercises 1.3 the fundamental theorem of ca
score: 195/260 answered: 20/26
evaluate the integral
\\(\int_{5}^{4} \sin(t) dt\\)

Explanation:

Step1: Recall antiderivative of $\sin(t)$

The antiderivative of $\sin(t)$ is $-\cos(t)$.

Step2: Apply Fundamental Theorem of Calculus

Use $\int_{a}^{b} f(t)dt = F(b)-F(a)$, where $F(t)=-\cos(t)$, $a=5$, $b=4$.
$\int_{5}^{4} \sin(t)dt = -\cos(4) - (-\cos(5))$

Step3: Simplify the expression

$\int_{5}^{4} \sin(t)dt = \cos(5) - \cos(4)$

Answer:

$\cos(5) - \cos(4)$