TS EAMCET · Maths · Area Under Curves
The area of the region bounded by \(y=x^3\), x -axis, \(x=-2\) and \(x=4\) is
- A 64
- B \(\frac{81}{4}\)
- C \(\frac{66}{5}\)
- D 68
Answer & Solution
Correct Answer
(D) 68
Step-by-step Solution
Detailed explanation
\(A = \int_{-2}^{0} (-x^3) dx + \int_{0}^{4} x^3 dx\) \(A = [-\frac{x^4}{4}]_{-2}^{0} + [\frac{x^4}{4}]_{0}^{4}\) \(A = (0 - (-\frac{16}{4})) + (\frac{256}{4} - 0)\) \(A = 4 + 64\) \(A = 68\)
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 \(\frac{3 x}{(x-a)(x-b)}=\frac{2}{x-a}+\frac{1}{x-b}\), then \(a: b\) is equal toTS EAMCET 2007 Medium
- The position vectors of \(P\) and \(Q\) are respectively \(\overrightarrow{\mathbf{a}}\) and \(\overrightarrow{\mathbf{b}}\). If \(\mathrm{R}\) is a point on \(\overrightarrow{\mathrm{PQ}}\) such that \(\overrightarrow{\mathrm{PR}}=5 \overrightarrow{\mathrm{PQ}}\), then the position vector of \(R\) isTS EAMCET 2008 Medium
- The period of \(\left(\tan \theta-\frac{1}{3} \tan ^3 \theta\right)\left(\frac{1}{3}-\tan ^2 \theta\right)^{-1}\) where \(\tan ^2 \theta \neq \frac{1}{3}\) isTS EAMCET 2010 Easy
- If \(\sqrt{2} \sin ^2 x+(3 \sqrt{2}+1) \sin x+3>0\) and \(x^2-7 x+10 < 0\), then \(x\) lies in the intervalTS EAMCET 2019 Easy
- If a normal chord of a parabola \(y^2=4 a x\) subtends a right angle at the origin, then the slope of that normal chord isTS EAMCET 2018 Medium
- The function that is not differentiable at \(x=1\) isTS EAMCET 2018 Medium
More PYQs from TS EAMCET
- If \(\int x(1+x) \log \left(1+x^2\right) d x=F(x)\) \(\log \left(1+x^2\right)-\frac{2}{3} \tan ^{-1} x-\frac{2 x^3}{9}-\frac{x^2}{2}+\frac{2 x}{3}+c\), then \(F(x)=\)TS EAMCET 2018 Hard
- Young's double slit experiment is carried out by using green, red and blue light, one colour at a time. The fringe width recorded are \(\beta_G\) \(\beta_R, \beta_B\) respectively, thenTS EAMCET 2020 Easy
- If the sum of two of the roots of \(x^3+p x^2-q x+r=0\) is zero, then \(p q\) is equal toTS EAMCET 2003 Easy
- Let \(I_n=\int \sec ^n x d x\). If \(5 I_6-4 I_4=f(x)\), then \(f\left(\frac{\pi}{4}\right)\) is equal toTS EAMCET 2020 Medium
- A body of mass \(2 \mathrm{~kg}\) starts from rest and moves with uniform acceleration. It acquires a velocity \(20 \mathrm{~ms}^{-1}\) in \(4 \mathrm{~s}\). The power exerted on the body in \(2 \mathrm{~s}\) in watts isTS EAMCET 2002 Easy
- An electromagnetic wave having frequency \(4 \times 10^{14} \mathrm{~Hz}\) is passing through a small volume. The energy contained in this volume oscillates with frequencyTS EAMCET 2018 Easy