Question
Using integration find the area of the triangular region whose sides have equations y = 2x + 1, y = 3x + 1 and x = 4.
✓
Answer
Getting the points of intersection as
A(0,1),B(4, 9) and C(4,13)
Area $\Delta$ ABC = $\int\limits_0^4\text{x}\text{(3x + 1)}\text{dx}-\int\limits_0^4\text{(2x + 1)}\text{dx}$
$=\int\limits_0^4\text{x dx}=\Bigg[\frac{\text{x}^{2}}{\text{2}}\Bigg]^4_0=8\text{sq. units}$.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Find the integrals of the functions in Exercises:
$\sin^{-1}(\cos\text{x})$
→$\sin^{-1}(\cos\text{x})$
Evaluate the following integrals:
$\int\frac{\cos^3\text{x}}{\sqrt{\sin\text{x}}}\text{dx}$
→$\int\frac{\cos^3\text{x}}{\sqrt{\sin\text{x}}}\text{dx}$
Find: $\int \frac{x \sin^{-1} x}{\sqrt{1 - x^{2}}} \text{d}x.$
→Determine the binomial distribution whose mean is 9 and variance $\frac{9}{4}.$
→Prove that the function $\text{f(x)}=\begin{cases}\frac{\sin\text{x}}{\text{x}},&\text{x}<0\\\text{x}+1,&\text{x}\geq0\end{cases}$ is everywhere continuous.
→Find the direction cosines of the line $\frac{\text{x}+2}{2}=\frac{2\text{y}-7}{6}=\frac{5-\text{z}}{6}.$ Also, find the vector equation of the line through the point A(-1, 2, 3) and parallel to the given line.
→Two schools P and Q want to award their selected students on the values of Discipline, Politeness and Punctuality. The school P wants to award ₹ x each, ₹ y each and ₹ z each the three respectively values to its 3, 2 and 1 students with a total award money of ₹ 1,000. School Q wants to spend ₹ 1,500 to award its 4, 1 and 3 students on the respective values (by giving the same award money for three values as before). If the total amount of awards for one prize on each value is ₹ 600, using matrices, find the award money for each value. Apart from the above three values, suggest one more value for awards.
A couple has two children. Find the probability that both the children are,
- Males, if it is known that at least one of the children is male.
- Females, if it is known that the elder child is a female.
A manufacturer of patent medicines is preparing a production plan on medicines, A and B. There are sufficient raw materials available to make 20000 bottles of A and 40000 bottles of B, but there are only 45000 bottles into which either of the medicines can be put. Further, it takes 3 hours to prepare enough material to fill 1000 bottles of A, it takes 1 hour to prepare enough material to fill 1000 bottles of B and there are 66 hours available for this operation. The profit is Rs. 8 per bottle for A and Rs. 7 per bottle for B. How should the manufacturer schedule his production in order to maximize his profit?
Solve the following initial value problems:
$\text{dy}=\cos\text{x}(2-\text{y cosecx})\text{dx}$
→$\text{dy}=\cos\text{x}(2-\text{y cosecx})\text{dx}$