MHT CET · Maths · Area Under Curves
The area of the region bounded by the curve \(y=4 x^{3}-6 x^{2}+4 x+1\) and the lines \(x=1, x=5\) and \(x\) axis is
- A 428 sq. units
- B 400 sq. units
- C 334 sq. units
- D 378 sq. units
Answer & Solution
Correct Answer
(A) 428 sq. units
Step-by-step Solution
Detailed explanation
(C)
Required area is shaded.
\(\begin{array}{l}
\int_{1}^{5} 4 x^{3}-6 x^{2}+4 x+1 d x \\
=\left[\frac{4 x^{4}}{4}-\frac{6 x^{3}}{3}+\frac{4 x^{2}}{2}+x\right]_{1}^{5} \\
=\left[x^{4}-2 x^{3}+2 x^{2}+x\right]_{1}^{5} \\
=\left[5^{4}-2(5)^{3}+2(5)^{2}+5\right]-\left[1^{4}-2(1)^{3}+2(1)^{2}+1\right] \\
=[625-250+50+5]-[1-2+2+1] \\
=430-2=428 \text { sq. units }
\end{array}\)
Required area is shaded.
\(\begin{array}{l}
\int_{1}^{5} 4 x^{3}-6 x^{2}+4 x+1 d x \\
=\left[\frac{4 x^{4}}{4}-\frac{6 x^{3}}{3}+\frac{4 x^{2}}{2}+x\right]_{1}^{5} \\
=\left[x^{4}-2 x^{3}+2 x^{2}+x\right]_{1}^{5} \\
=\left[5^{4}-2(5)^{3}+2(5)^{2}+5\right]-\left[1^{4}-2(1)^{3}+2(1)^{2}+1\right] \\
=[625-250+50+5]-[1-2+2+1] \\
=430-2=428 \text { sq. units }
\end{array}\)
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 \(\bar{a}, \bar{b}, \bar{c}\) are non \(-\) coplanar vectos and \((\overline{\mathrm{a}}+\overline{\mathrm{b}}+\overline{\mathrm{c}}) \cdot(\overline{\mathrm{a}} \times \overline{\mathrm{b}}+\overline{\mathrm{b}} \times \overline{\mathrm{c}}+\overline{\mathrm{c}} \times \overline{\mathrm{a}})=\mathrm{k}[\overline{\mathrm{a}} \overline{\mathrm{b}} \overline{\mathrm{c}}]\),
then value of \(\mathrm{k}\) isMHT CET 2020 Medium - \(\sec 2 \theta-\tan 2 \theta=\)MHT CET 2020 Easy
- If the lines given by \(\bar{r}=2 \hat{\imath}+\lambda(\hat{\imath}+2 \hat{\jmath}+m \hat{k})\) and \(\bar{r}=\hat{\imath}+\mu(2 \hat{\imath}+\hat{\jmath}+6 \hat{k})\) are
perpendicular, then the value of \(m\) isMHT CET 2020 Easy - If \(y=\sin ^2\left(\cot ^{-1} \sqrt{\frac{1+x}{1-x}}\right)\), then \(\frac{\mathrm{d} y}{\mathrm{~d} x}\) has the valueMHT CET 2024 Medium
- The equation of a circle passing through origin and making \(\mathrm{x}\) -intercept 3 and \(\mathrm{y}\) - intercept \(-5\) isMHT CET 2020 Medium
- The equation of the line, through \(A(1,2,3)\) and perpendicular to the vector \(2 \hat{i}+\hat{j}-\hat{k}\) and \(\hat{i}+3 \hat{j}+2 \hat{k}\), isMHT CET 2024 Easy
More PYQs from MHT CET
- Identify the product \((\mathrm{X})\) formed in the following reaction.
\(
\mathrm{C}_6 \mathrm{H}_5 \mathrm{OH}+\mathrm{CH}_3 \mathrm{COOH} \stackrel{\mathrm{H}^{+}}{\rightleftharpoons} \mathrm{X}
\)MHT CET 2021 Easy - In common emitter mode of a transistor, the current gain is 8 . The input impedance is \(25 \mathrm{k} \Omega\) and load resistance is \(75 \mathrm{k} \Omega\). The power gain isMHT CET 2025 Medium
- Which from following monomers is used to obtain polymer represented asMHT CET 2024 Medium
- The general solution of the differential equation \(\frac{1}{x} \frac{\mathrm{~d} y}{\mathrm{~d} x}=\tan ^{-1} x\) isMHT CET 2024 Medium
- The electron in hydrogen atom is initially in the third excited state. When it finally moves to ground state, the maximum number of spectral lines emitted areMHT CET 2021 Easy
- Plasma cells are derived fromMHT CET 2015 Medium