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# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

$\int_3^{-2}\left(\sin\left(t\right)\right)dt$

Learn how to solve definite integrals problems step by step online.

$-\int_{-2}^{3}\sin\left(t\right)dt$

Learn how to solve definite integrals problems step by step online. Integrate sin(t) from 3 to -2. Since the upper limit of the integral is less than the lower one, we can rewrite the limits by applying the inverse property of integration limits: If we invert the limits of an integral, it changes sign: \int_a^bf(x)dx=-\int_b^af(x)dx. Apply the integral of the sine function. Evaluate the definite integral. Simplifying.

$-\frac{17}{30}$$\,\,\left(\approx -0.5666666666666667\right)$

### Problem Analysis

$\int_3^{-2}\left(\sin\left(t\right)\right)dt$

### Main topic:

Definite integrals

~ 0.41 seconds