KCET · Maths · Area Under Curves
The area of the region bounded by the curve \( y=\cos x \) between \( x=0 \) and \( x=\pi \) is
- A \( 1 \) sq. unit
- B \( 4 \) sq. unit
- C \( 2 \) sq. unit
- D \( 3 \) sq. unit
Answer & Solution
Correct Answer
(C) \( 2 \) sq. unit
Step-by-step Solution
Detailed explanation
Given curve, \( y=\cos x \) between \( x=0 \) and \( x=\pi \)
So, required area is given by
\[
\begin{array}{l}
\int_{0}^{\pi}|\cos x| d x=\int_{0}^{\pi / 2}(\cos x) d x+\int_{\pi / 2}^{\pi}(-\cos x) d x \\
\int_{0}^{\pi}|\cos x| d x=\left.(\sin x)\right|_{0} ^{\pi / 2}+.\left.(-\sin x)\right|_{\Pi / 2} ^{\Pi} \\
=1+1=\text { 2sq.units. }
\end{array}
\]
So, required area is given by
\[
\begin{array}{l}
\int_{0}^{\pi}|\cos x| d x=\int_{0}^{\pi / 2}(\cos x) d x+\int_{\pi / 2}^{\pi}(-\cos x) d x \\
\int_{0}^{\pi}|\cos x| d x=\left.(\sin x)\right|_{0} ^{\pi / 2}+.\left.(-\sin x)\right|_{\Pi / 2} ^{\Pi} \\
=1+1=\text { 2sq.units. }
\end{array}
\]
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- If \(x+i y=(-1+i \sqrt{3})^{2010}\), then \(x\) isKCET 2010 Easy
- If \( y=\log \left(\frac{1-x^{2}}{1+x^{2}}\right) \), then \( \frac{d y}{d x} \) is equal toKCET 2015 Hard
- The number of \( 4 \) digit numbers without repetition that can be formed using the digits \( 1,2,3,4 \),
\( 5,6,7 \) in which each number has two odd digits and two even digits isKCET 2019 Easy - If \( |x+5| \geq 10 \) thenKCET 2018 Easy
- \(\lim _{x \rightarrow 0} \frac{x 2^{x}-x}{1-\cos x}\) is equal toKCET 2012 Easy
- The number of solutions for the equation \(\sin 2 x+\cos 4 x=2\) isKCET 2008 Easy
More PYQs from KCET
- The value of \(\tan ^{-1}\left(\frac{x}{y}\right)-\tan ^{-1}\left(\frac{x-y}{x+y}\right)\) (where, \(x, y>0\) ) isKCET 2013 Easy
- The sum of two positive numbers is given. If the sum of their cubes is minimum, thenKCET 2012 Hard
- A toroid has \( 500 \) turns per metre length. If it carries a current of \( 2 \mathrm{~A} \), the magnetic energy density inside the toroid isKCET 2019 Medium
- \(80 \mathrm{~g}\) of oxygen contains as many atoms as inKCET 2008 Easy
- The size of the image of an object, which is at infinity, as formed by a convex lens of focal length \(30 \mathrm{~cm}\) is \(2 \mathrm{~cm}\). If a concave lens of focal length \(20 \mathrm{~cm}\) is placed between the convex lens and the image at a distance of \(26 \mathrm{~cm}\) from the lens, the new size of the image isKCET 2021 Easy
- A \(220 \mathrm{~V}\) AC supply is connected between points \(A\) and \(B\) as shown in figure, what will be the potential difference \(V\) across the capacitor?
KCET 2020 Easy