Holooly Plus Logo

Question 13.7: Evaluate (a) ∫²1 x² + 1 dx  (b) ∫¹2 x² + 1 dx (c) ∫^π 0 sin ......


(a) \int_1^2 x^2+1 d x          (b) \int_2^1 x^2+1 d x           (c)  \int_0^\pi \sin x d x

The 'Blue Check Mark' means that this solution was answered by an expert.
Learn more on how do we answer questions.

(a) Let I stand for  \int_1^2 x^2+1 d x.

I=\int_1^2 x^2+1 \mathrm{~d} x=\left[\frac{x^3}{3}+x\right]_1^2

The integral is now evaluated at the upper and lower limits. The difference gives the value required.


(b) Because interchanging the limits of integration changes the sign of the integral, we find

\int_2^1 x^2+1 \mathrm{~d} x=-\int_1^2 x^2+1 \mathrm{~d} x=-\frac{10}{3}

(c) \int_0^\pi \sin x d x=[-\cos x]_0^\pi=(-\cos \pi)-(-\cos 0)=1-(-1)=2

Figure 13.10 illustrates this area.

Screenshot 2023-02-17 181426

Related Answered Questions

Question: 13.11

Verified Answer:

Figure 13.13 illustrates the required area. From t...
Question: 13.9

Verified Answer:

Figure 13.11 illustrates the required area. [latex...
Question: 13.8

Verified Answer:

\begin{aligned}\text { Area } & =\int_1...
Question: 13.6

Verified Answer:

(a) Using the identities in Table 3.1 we find [lat...
Question: 13.5

Verified Answer:

Powers of trigonometric functions, for example  [l...
Question: 13.2

Verified Answer:

From Table 10.1 we find \frac{\mathrm{d}}{\...
Question: 13.1

Verified Answer:

We need to find a function which, when differentia...