Question

Math

Posted 3 months ago

```
$\int_{0}^{5}[g(x)+h(x)] d x=$
```

Sign in to unlock the answer

Answer from Sia

Posted 3 months ago

Solution by Steps

step 1

We need to evaluate the definite integral $\int_{0}^{5}[g(x)+h(x)] \, dx$

step 2

From the given information, the area under $g(x)$ from $0$ to $5$ is $4$

step 3

Similarly, the area under $h(x)$ from $0$ to $5$ is $-8$

step 4

To find the integral of $g(x) + h(x)$ from $0$ to $5$, we add the areas under $g(x)$ and $h(x)$ over this interval: $4 + (-8)$

step 5

Simplifying, we get $4 - 8 = -4$

Answer

$\int_{0}^{5}[g(x)+h(x)] \, dx = -4$

Key Concept

Definite Integral of Sum of Functions

Explanation

The integral of the sum of two functions over an interval is the sum of the integrals of the individual functions over that interval.

Not the question you are looking for? Ask here!

Enter question by text

Enter question by image

Upgrade to Asksia Pro

Join a AskSia's Pro Plan, and get 24/7 AI tutoring for your reviews, assignments, quizzes and exam preps.

Unlimited chat query usages

Strong algorithms that better know you

Early access to new release features

Study Other Question