Calculus

Integrals

Medium

applied

If the manufacturer's marginal cost function is $100\left(\frac{1}{\sqrt{x}}+50\right)$ , then the cost involved to increase production from 25 units to 100 units is:

₹3,00,000

₹2,75,000

₹3,76,000

₹2,80,000

✅ Correct Option: 3

Cost $=\int_{25}^{100}100\left(\frac{1}{\sqrt x}+50\right)dx=100\left[2\sqrt x+50x\right]_{25}^{100}=100[(20+5000)-(10+1250)]=100(3760)=376000$ .

2026: 30 May Shift 1

$\int_{-2}^{1}|x^2-1|dx$ equals:

2025: 27 May Shift 1

The value of $\int \frac{x^5}{\sqrt{1 + x^3}} dx$ is

2026: 18 May Shift 1

Match List-I with List-II

List-I	List-II
Integral	Value of the integral
(A) $\displaystyle\int_{1}^{2} e^{2\log x} \, dx$	(I) $\log 2$
(B) $\displaystyle\int_{-1}^{1} \left\vert x \right\vert \, dx$	(II) $\dfrac{1}{2}$
(C) $\displaystyle\int_{0}^{1} \log e^x \, dx$	(III) $\dfrac{7}{3}$
(D) $\displaystyle\int_{1}^{2} \dfrac{1}{x} \, dx$	(IV) $1$

Choose the correct answer from the options given below:

2025: 14 May Shift 2

For $x \in \mathbb{R} - \{-1,0,1\}$ , $\int \frac{1}{x - x^5}dx$ is equal to

2026: 31 May Shift 2

In which of the following cases the value of the integral is more than 10?

A. $\displaystyle\int_0^2 |x|\,dx$

B. $\displaystyle\int_0^2 (x+3)^2\,dx$

C. $\displaystyle\int_0^2 e^x\,dx$

D. $\displaystyle\int_0^2 (2x+5)\,dx$

Choose the correct answer from the options given below:

2025: 26 May Shift 2

$\int \frac{(x-1)e^x}{x^2} dx, x > 0$ equals (where C is an arbitrary constant)

If the manufacturer's marginal cost function is 100(1x+50)100\left(\frac{1}{\sqrt{x}}+50\right)100(x​1​+50), then the cost involved to increase production from 25 units to 100 units is: